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Trigonometry worksheet

Grades 10–11 · CCSS HSG.SRT.C.6, HSF.TF.A.2, HSF.TF.A.3

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Calculate: Inverse (angle from a value)
- Inverse function: arcsin
- Value: 0.7
Find: arcsin(0.7) in degrees
Answer
2.
Problem 2.
- Calculate: Inverse (angle from a value)
- Inverse function: arctan
- Value: 0.6
Find: arctan(0.6) in degrees
Answer
3.
Problem 3.
- Calculate: Trig functions of an angle
- Function: Tangent (tan)
- Angle: 24 degrees
Find: Tangent (tan)
Answer
4.
Problem 4.
- Calculate: Trig functions of an angle
- Function: Secant (sec)
- Angle: 20 degrees
Find: Secant (sec)
Answer
5.
Problem 5.
- Calculate: Inverse (angle from a value)
- Inverse function: arctan
- Value: 0.4
Find: arctan(0.4) in degrees
Answer
6.
Problem 6.
- Calculate: Inverse (angle from a value)
- Inverse function: arcsin
- Value: 0.6
Find: arcsin(0.6) in degrees
Answer
7.
Problem 7.
- Calculate: Trig functions of an angle
- Function: Secant (sec)
- Angle: 24 degrees
Find: Secant (sec)
Answer
8.
Problem 8.
- Calculate: Trig functions of an angle
- Function: Secant (sec)
- Angle: 25 degrees
Find: Secant (sec)
Answer
9.
Problem 9.
- Calculate: Trig functions of an angle
- Function: Secant (sec)
- Angle: 45 degrees
Find: Secant (sec)
Answer
10.
Problem 10.
- Calculate: Inverse (angle from a value)
- Inverse function: arccos
- Value: 0.6
Find: arccos(0.6) in degrees
Answer

Answer key: Trigonometry worksheet

1. arcsin(0.7) in degrees: 44.43 °
1. arcsin works backward: it gives the angle whose sin is your value. It uses the standard main answer, in the range −90° to 90°
  $\arcsin (0.7)$ $= 44.4270040008 °$
2. Convert to radians: multiply by π ÷ 180
  $44.4270040008 \times \frac{π}{180}$ $= 0.7753974966$
2. arctan(0.6) in degrees: 30.96 °
1. arctan works backward: it gives the angle whose tan is your value. It uses the standard main answer, in the range between −90° and 90°
  $\arctan (0.6)$ $= 30.9637565321 °$
2. Convert to radians: multiply by π ÷ 180
  $30.9637565321 \times \frac{π}{180}$ $= 0.5404195003$
3. Tangent (tan): 0.45
1. Start from the sine and cosine of the angle
  $\sin (24 °) = 0.4067366431, \cos (24 °) = 0.9135454576$
2. Tangent is sine divided by cosine
  $\tan (24 °)$ $= \frac{0.4067366431}{0.9135454576}$ $= 0.4452286853$
4. Secant (sec): 1.06
1. Start from the sine and cosine of the angle
  $\sin (20 °) = 0.3420201433, \cos (20 °) = 0.9396926208$
2. Secant is 1 divided by cosine
  $\sec (20 °)$ $= \frac{1}{0.9396926208}$ $= 1.0641777725$
5. arctan(0.4) in degrees: 21.8 °
1. arctan works backward: it gives the angle whose tan is your value. It uses the standard main answer, in the range between −90° and 90°
  $\arctan (0.4)$ $= 21.8014094864 °$
2. Convert to radians: multiply by π ÷ 180
  $21.8014094864 \times \frac{π}{180}$ $= 0.3805063771$
6. arcsin(0.6) in degrees: 36.87 °
1. arcsin works backward: it gives the angle whose sin is your value. It uses the standard main answer, in the range −90° to 90°
  $\arcsin (0.6)$ $= 36.8698976458 °$
2. Convert to radians: multiply by π ÷ 180
  $36.8698976458 \times \frac{π}{180}$ $= 0.6435011088$
7. Secant (sec): 1.09
1. Start from the sine and cosine of the angle
  $\sin (24 °) = 0.4067366431, \cos (24 °) = 0.9135454576$
2. Secant is 1 divided by cosine
  $\sec (24 °)$ $= \frac{1}{0.9135454576}$ $= 1.0946362785$
8. Secant (sec): 1.1
1. Start from the sine and cosine of the angle
  $\sin (25 °) = 0.4226182617, \cos (25 °) = 0.906307787$
2. Secant is 1 divided by cosine
  $\sec (25 °)$ $= \frac{1}{0.906307787}$ $= 1.103377919$
9. Secant (sec): 1.41
1. Start from the sine and cosine of the angle
  $\sin (45 °) = 0.7071067812, \cos (45 °) = 0.7071067812$
2. Secant is 1 divided by cosine
  $\sec (45 °)$ $= \frac{1}{0.7071067812}$ $= 1.4142135624$
10. arccos(0.6) in degrees: 53.13 °
1. arccos works backward: it gives the angle whose cos is your value. It uses the standard main answer, in the range 0° to 180°
  $\arccos (0.6)$ $= 53.1301023542 °$
2. Convert to radians: multiply by π ÷ 180
  $53.1301023542 \times \frac{π}{180}$ $= 0.927295218$