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Right Triangle Trigonometry

Honors Precalculus

Mr. Velazquez

Right Triangles and Trigonometry

Right Triangles and Trigonometry

Trig values for a given angle are always the same, no matter how large the triangle is, due to the Law of Similar Triangles.

Right Triangles and Trigonometry

Find the value of each of the six trigonometric functions for 𝜃 if 𝑏 = 4 and 𝑐 = 2 5.

4b

2 5c

Right Triangles and Trigonometry

Find the value of 𝑏 and 𝑐 if ∠𝐶 = 30°.

B

A C

18

b

c

Right Triangles and Trigonometry

Find the value of the six trigonometric functions for ∠𝐺

Trig Functions for Any Angle

Trigonometry of Complements

Find a cofunction with the same value as the following expressions:

cos 20° cot 40°

Signs of Trigonometric Functions

ALL STUDENTS

TAKE CALCULUS

Signs of Trigonometric Functions

Name the quadrant in which 𝜃 lies if:

(a) tan 𝜃 is positive and sin 𝜃 is negative

(b) csc 𝜃 is positive and cos 𝜃 is positive

(c) sec 𝜃 is negative and cot 𝜃 is negative

Reference Angles

Using Reference Angles

Using Reference Angles

Use reference angles to find the exact values for each of the following functions:

(a) sin 4𝜋

3

(b) cos 7𝜋

6

(c) tan −120°

Using Reference Angles

Use reference angles to find the exact values for each of the following functions:

(a) sec 7𝜋

3

(b) csc 13𝜋

6

(c) cot 405°

Exit Ticket/Homework

PART 1:

The distance 𝑎 across the pond is unknown. To find this distance, a surveyor took the measurements shown. Find 𝑎.

1200 yards

PART 2:

For each angle below, find a reference angle 𝜃′ and use it to give the values of the six trig functions.

(a) 𝜃1 =15𝜋

6 (b) 𝜃2 = −

5𝜋

4 (c) 𝜃3 = 420°

HOMEWORK: (due Jan 19) Pg. 513, #4-80 (mult. of 4)