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Sine and Cosine Rules and Area of Triangles
Learners discover how to find missing sides and angles using trigonometry. Scholars first watch a video covering the Law of Sines and Cosines, as well as the area formula for a triangle. To test their knowledge, they complete a activity...
Illustrative Mathematics
Sum and Difference Angle Formulas
Need practice deriving trigonometric angle formulas? With this worksheet, pupils derive the sum and difference formulas for cosine and tangent and the difference formula for sine. Scholars use the sine sum formula and other known...
Concord Consortium
Adding the Sines
It's a sign! Scholars analyze sine functions for patterns in their periods. The exploration advances beyond a simple function to the combination of two functions with even and odd coefficients. Their goal is to find a pattern between the...
EngageNY
Addition and Subtraction Formulas 2
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...
Concord Consortium
Sine Solution
How many times can eager mathematicians catch the waves? Pupils find the solutions of three different trigonometric equations. They then determine the effect of the slope of a line that intersects a trigonometric function and the number...
EngageNY
Mid-Module Assessment Task: Pre-Calculus Module 4
Challenge scholars to show what they know about properties and addition and subtraction formulas for trigonometric functions. The resource provides a mid-unit check on the progress toward mastery of trigonometric concepts. The areas...
EngageNY
End-of-Module Assessment Task: Pre-Calculus Module 4
Challenge your scholars to show what they know about the Law of Sines, Law of Cosines, and inverses. The six-question assessment is the last in a series of 16. Pupils find the area of triangles and show that the Law of Sines and Law of...
EngageNY
End-of-Module Assessment Task - Geometry (module 2)
Increase the level of assessment rigor with the test of performance tasks. Topics include similar triangles, trigonometric ratios, Law of Sines, Law of Cosines, and trigonometric problem solving.
EngageNY
Exploiting the Connection to Trigonometry 1
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex...
EngageNY
Matrix Notation Encompasses New Transformations!
Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different...
EngageNY
An Area Formula for Triangles
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
Illustrative Mathematics
Calculations with Sine and Cosine
Practice makes perfect and perfecting those trigonometric functions are vital in trigonometry. The task requires evaluating cosine and sine values at common degree measures before looking at the results. Is there a pattern when the...
Illustrative Mathematics
Trigonometric Ratios and the Pythagorean Theorem
Take an alternative route with trigonometry and let learners connect a tweaked version of the pythagorean theorem to the original in terms of triangle sides. The assignment leads participants towards deriving the Pythagorean identity...
Illustrative Mathematics
Finding Trig Values
Let's keep trigonometry simple. When given a cosine ratio, learners must use the clues about the quadrant to determine the sine and tangent ratios. The answer key has a complete worked-out solution to help guide pupils through the...
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Illustrative Mathematics
Exploring Sinusoidal Functions
What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...
EngageNY
Algebra II Module 2: Mid-Module Assessment
Time for classes to show what they've learned. Use several tasks to assess understanding of the trigonometric functions, unit circle, radians, and basic trigonometric identities.
EngageNY
Modeling Video Game Motion with Matrices 2
The second day of a two-part instructional activity on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in...
EngageNY
Revisiting the Graphs of the Trigonometric Functions
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
EngageNY
Inverse Trigonometric Functions
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th lesson of a 16-part series. They use inverse functional...
Curated OER
Sum and Difference angle formulas
Learners use the sum angle formula for sine to derive the sum and difference formulas for cosine and tangent. The level of difficulty is quite high. Learners must be familiar with trigonometric identities as well as the characteristics...
Curated OER
Minimal Pair Quiz: Ee vs. I
In this /ee/ vs. /i/ worksheet, 4th graders choose the correct word to complete 20 sentences using words that sound almost the same, with immediate online feedback.
Khan Academy
Khan Academy: Solve Sinusoidal Equations (Basic)
Solve equations of the form sin(x)=d or cos(x)=d where d is any number. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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