Download 25.  27.  SOLUTION:  

Study Guide and Review - Chapter 4
Sketch each angle. Then find its reference
angle.
25. 240
Find the exact values of the five remaining
trigonometric functions of θ.
29. cos
= , where sin
> 0 and tan > 0
SOLUTION: The terminal side of 240º lies in Quadrant III.
Therefore, its reference angle is ' = 240 – 180
or 60º.
SOLUTION: To find the other function values, find the
coordinates of a point on the terminal side of .
Because sin θ and tan are positive, must lie in
Quadrant I. This means that both x and y are
positive.
= Because cos
or , x =2 and r = 5. Find y.
27. Use x = 2, y =
, and r = 5 to write the five
remaining trigonometric ratios.
SOLUTION: lies in Quadrant III. The terminal side of
Therefore, its reference angle is
' =
.
31. where cos
> 0 and cot < 0
SOLUTION: where cos
Find the exact values of the five remaining
trigonometric functions of θ.
29. cos
= , where sin
> 0 and tan > 0
SOLUTION: To find the other function values, find the
coordinates of a point on the terminal side of .
Because sin θ and tan are positive, must lie in
Quadrant I. This means that both x and y are
positive.
= Because cos
or , x =2 and r = 5. Find y.
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> 0 and cot < 0
To find the other function values, find the
coordinates of a point on the terminal side of .
Because cos θ is positive and cot θ is negative,
must lie in Quadrant IV. This means that x is
positive and y is negative.
Because sin
= or –
, y = –5 and r = 13.
Find x.
Use x = 12, y = –5, and r = 13 to write the five
remaining trigonometric ratios.
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Study Guide and Review - Chapter 4
31. where cos
> 0 and cot < 0
34. cot
SOLUTION: SOLUTION: where cos
lies in Quadrant IV, the reference angle θ' of is > 0 and cot < 0
Because the terminal side of
.
To find the other function values, find the
coordinates of a point on the terminal side of .
Because cos θ is positive and cot θ is negative,
must lie in Quadrant IV. This means that x is
positive and y is negative.
Because sin
= or –
, y = –5 and r = 13.
Find x.
In quadrant IV cot θ is negative.
Use x = 12, y = –5, and r = 13 to write the five
remaining trigonometric ratios.
35. sec 450
SOLUTION: Find the exact value of each expression. If undefined, write undefined.
33. sin 180
Because the terminal side of lies on the positive yaxis, the reference angle ' is .
SOLUTION: Because the terminal side of lies on the negative x-axis, the reference angle ' is 180°.
34. cot
36. SOLUTION: eSolutions Manual - Powered by Cognero
Because the terminal side of
lies in Quadrant IV, the reference angle θ' of is .
SOLUTION: Page 2
Because the terminal side of θ lies in Quadrant III,
Study Guide and Review - Chapter 4
36. SOLUTION: Because the terminal side of θ lies in Quadrant III,
the reference angle θ' of is .
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