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Trigonometric Functions: Finding Values from Given Points and Angles (Exercise Set 4), Study notes of Trigonometry

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

2021/2022

Uploaded on 09/27/2022

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Review Exercise Set 4
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.
3
cos sin 0
7and
θθ
= <
Exercise 3: Using the given conditions, find the exact value of each of the remaining trigonometric
functions of θ.
cot 3 cos 0and
θθ
= <
pf3
pf4
pf5

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Review Exercise Set 4

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

θ= and θ<

Exercise 3: Using the given conditions, find the exact value of each of the remaining trigonometric functions of θ.

cot θ= 3 and cos θ< 0

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.

cot θ= 3 and cos θ< 0

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

 π π + π^ = ^  +

   ^ 