Name _______________________
Cofunctions PRACTICE
DIRECTIONS: Find the value of x in each expression.
1. sin80 = cos x x = ________
4. cos 75 = sin x x = ________
2. sin 50 = cos x
x = ________
5. sin88 = cos x
x = ________
3. cos83 = sin x
x = ________
6. cos 74 = sin x
x = ________
DIRECTIONS: Fill in the blank with an equivalent expression.
7. sin 47 = _________
10. cos 71 = _________
8. cos32 = _________
11. cos12 = _________
9. sin 45 = _________
12. sin 68 = _________
DIRECTIONS: Solve for x .
13. sin(63) = cos(2x − 3)
14. sin(x +15) = cos(2x)
15. cos x = sin(2x)
1
16. The degree measure of an angle in a right triangle is x , and sin x = . Which of these
3
1
expressions is also equal to ? Select all that apply.
3
£ A. cos x
£ B. cos(x − 45)
£ C. cos(45 − x)
£ D. cos(60 − x)
£ E. cos(90 − x)
17. In a right triangle, m∠B ≠ m∠C . Let sin B = r and cos B = s . What is sinC − cosC ?
A. r + s
1.
B. r − s
C. s − r
D.
r
s
Lesson 51 ADDITIONAL PRACTICE
1. Mariela is standing in a building and looking out of a window at a tree. The tree is 20 feet
away from Mariela. Mariela’s line of sight to the top of the tree creates a 42° angle of
elevation, and her light of sight to the base of the tree creates a 31° angle of depression.
What is the height, to the nearest foot, of the tree?
2. Two buildings on opposite sides of a street are 40 m apart. From the top of the taller
building, which is 185 m high, the angle of depression to the top of the shorter building is
13°. Find the height of the shorter building. Round to the nearest integer.
3. Martha is 180 cm tall and her daughter Heidi is just 90 cm tall. Who casts the longer
shadow, Martha when the sun is 70° above the horizon, or Heidi when the sun is 35°
above the horizon? How much longer? Round to the nearest integer.
4. A rhombus has diagonals of length 4 and 10. Find the four interior angles of the rhombus
to the nearest degree.
Cofunctions Practice – ANSWERS
1. sin80 = cos x x = 10°
2. sin 50 = cos x x = 40°
3. cos83 = sin x x = 7°
4. cos 75 = sin x x = 15°
5. sin88 = cos x x = 2°
6. cos 74 = sin x x = 16o
7. sin 47 = cos 33
8. cos32 = sin 58
10. cos 71 = sin 19
11. cos12 = sin 78
12. sin 68 = cos 22
9. sin 45 = cos 45
13. sin(63) = cos(2x − 3)
x = 15
14. sin(x +15) = cos(2x)
15. cos x = sin(2x)
x = 30
x = 25
1
16. The degree measure of an angle in a right triangle is x , and sin x = . Which of these
3
1
expressions is also equal to ? Select all that apply.
3
£ A. cos x
£ B. cos(x − 45)
£ C. cos(45 − x)
£ D. cos(60 − x)
R E. cos(90 − x)
17. In a right triangle, m∠B ≠ m∠C . Let sin B = r and cos B = s . What is sinC − cosC ?
A. r + s
B. r − s
C.
s−r
Lesson 51 Additional Practice – ANSWERS
1. The height of the tree is approximately 30 feet.
2. The height of the shorter building is approximately 176 meters.
3. Heidi casts the longer shadow by approximately 63 centimeters.
4. The angles of the rhombus are approximately 44°, 44°, 136°, and 136°.
D.
r
s