Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Solutions to Exercise Set 4 of a trigonometry course, which involves finding the values of the six trigonometric functions (sin, cos, tan, csc, sec, cot) for given points and angles. The solutions include step-by-step calculations and visual representations.
Typology: Study notes
1 / 7
This page cannot be seen from the preview
Don't miss anything!
Exercise 1: If the point (-3, 7) is a point on the terminal side of angle θ then find the exact value of each of the six trigonometric functions of θ.
Exercise 2: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ.
cos 3 sin 0 7
Exercise 3: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ.
Exercise 4: Use reference angles to find the value of the given expression.
cos 495°
Exercise 5: Find the exact value of the given expression. Write the answer as a single fraction.
cos 5 cot 5 sin^3 3 6 4
π π + π
Exercise 2: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ.
cos 3 sin 0 7
θ= and θ<
Graph the angle θ based on the given conditions to get a visual picture of the problem
Find the length of the side "y"
( ) ( )
2 2 2 (^2 2 ) 2 2
r x y y y y y y
Remember since the point is in the fourth quadrant y must be negative.
Find the value of the remaining trig functions
sin
2 10 7 2 10 7
y r
cos 3 7
x r
tan
2 10 3 2 10 3
y x
θ =
Exercise 2 (Continued):
csc
7 2 10 7 10 20
r y
θ =
sec 7 3
r x
cot
3 2 10 3 10 20
x y
θ =
Exercise 3: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ.
Graph the angle θ based on the given conditions to get a visual picture of the problem
Since cosine is negative and cotangent is positive x and y must both be negative which would put the angle in the third quadrant.
cot 3 3 1
x y
θ = = − = −
Find the length of the hypotenuse "r"
( ) ( )
2 2 2
3 2 12 9 1 10 10
r x y
r
Exercise 4 (Continued):
cos 495 1 2 2 2
Exercise 5: Find the exact value of the given expression. Write the answer as a single fraction.
cos 5 cot 5 sin^3 3 6 4
cos 5 cot 5 sin 3 3 3 2 3 6 4 2 2 3 2 2 2 3 2 2
