Angle Teacher Resources
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This video introduces the basics of trigonometry. It starts by defining a right triangle and showing two different examples of finding the ratios of sine, cosine, and tangent using the SOH-CAH-TOA mnemonic. This resource could be used as a quick introduction or review.
Basic Trigonometry ll
Sal continues with examples of finding the sine, cosine, and tangent of an angle in a right triangle using SOH-CAH-TOA. In his examples, he reviews the use of the Pythagorean Theorem and rationalizing the denominator of a fraction. He also does an example of traditional 30-60-90 triangle and finds each of the three trigonometric ratios for the 30_ and 60_ angles. Note: After watching this video, there is a set of practice problems, titled ï¿½Trigonometry 1ï¿½, that would be worth trying.
IIT JEE Trigonometry Maximum
Sal solves a question from a college entrance exam in India which asks one to find the maximum value of a rational expression with trigonometry ratios. To solve this problem, Sal finds a maximum value by finding the minimum value of the denominator. He uses trigonometric identities to simplify the expression and then finds where the derivative of the denominator is zero and answers the questions whether or not it is a minimum or maximum value. This is an interesting problem that mixes trigonometry and calculus skills.
Proof: sin(a+b)=(cos a)(sin b)+(sin a)(cos b)
Sal proves the sum of angles formula for sine, sin (a+ b) = cos (a) sin (b) + sin (a) cos (b), through a clear but rather non-intuitive proof. The proof is interesting as it not only uses the SOH-CAH-TOA model but requires one to recall some interesting geometric properties of parallel lines and angles. A challenging problem after watching this video would be try to prove the cosine version of this identity, which is shown in another video.
Proof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)
Using a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof the cosine sum of angles formula, cos (a+ b) = cos (a) cos (b) - sin (a) sin (b). This proof also uses the SOH-CAH-TOA model and some interesting geometric properties of parallel lines and angles.
This unit covers the basic trigonometry including understanding radians, how to convert between radians and degrees, the area of a circle subtended by an angle, basic properties and graphs of sine, cosine, tangent, and solving trigonometric equations. Activities, problem sets, and answers are given.
Students identify the different ratios of a right triangle. In this trigonometry activity, students calculate the sine, cosine and tangent of a right triangle. They differentiate between right and oblique triangles.
Extending Trigonometry Skills
In this trigonometry learning exercise, students use the sine and cosine law to solve problems. They investigate obtuse triangles using these laws. There are 40 questions.
Applied Trigonometry Problems
In this applied trigonometry problems worksheet, students solve 12 short answer word problems. Students use trigonometric ratios to find angles of elevation and depression. Students find distances between objects using trigonometric ratios and angles of elevation and depression.
In this trigonometry activity, students solve and complete 5 various types of problems. First, they find the exact ratios for each trigonometric function. Then, students use the expansion to find the exact value of a given trig function. They also solve the equations shown by restricting their answers.
IIT JEE Trigonometry Problem 1
Sal solves an interesting question in this video from a college entrance exam in India that requires one to use knowledge of arithmetic progressions, trigonometric identities, and algebra. He works through solving the problem in a step-by-step fashion by talking through his thought process in order to help one follow the solution as well as understand why certain steps are taken.
IIT JEE Trigonometry Constraints
Sal solves a challenging trigonometric problem for finding the number of values of _ that satisfy a number of constraints over a given interval. He shows a clear step-by-step solution and uses some trigonometric identities that he derives.
Scoring Guide for the Algebra 2/Trigonometry Test Sampler
Pupils take an Algebra II/Trigonometry sample test. In this Algebra II/Trigonometry sample sample test lesson, students take a sample test for Algebra 2/Trigonometry. Pupils solve 39 multiple choice/short answer questions about topics including radicals, equations of circles, exponential equations, angle measures, etc.
Exploration of Trigonometry
Learners explore how changing an angle in a triangle changes the ratio of the sides. They also explore how changing the sides can make changes to an angle in a triangle. Finally, they determine how two different pairs of sides, in the same ratio, will give them the same angle.
Review of Trigonometry
In this review of trigonometry activity, students determine the values of angels using sine, cosine, and tangent. They determine arc length and find the coordinates of endpoints. This two-page activity contains approximately 70 problems.
Third graders identify and construct right, acute and obtuse angles and begin to appreciate the degree and unit of measurement of angle. They know the degree value of angles that are simple fractions of a whole turn know that the angle at a point is 360++
In this trigonometry worksheet, students solve for trigonometric functions. They convert between radians and angles using the properties of sine, cosine and tangent. There are 30 problems on this handout.
Trigonometry for AC Circuits
In this physics worksheet, students solve 23 trigonometry based problems. Students apply the Pythagorean Theorem in electricity calculations.
Angles in Standard Positions
Students identify positive and negative angles using the Unit Circle. In this pre-calculus instructional activity, students identify the different angles on a unit circle using the coordinate plane and the four different quadrants as a guide. They calculate the basic trigonometric functions.
Students experience real life situations where trigonometry is used on a daily basis. They utilize trigonometry to the solving of application problems that involve the calculating of the sine, cosine, and tangents of a given angle as well as the finding of the length of a missing side of a right triangle given an angle and a side.