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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.
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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