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)