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  1. Problems
  2. /Trigonometry

Trigonometry

Mathematics
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33 problems
Type:
1.
Show that cos 20° cos 40° cos 80° = 1/8, and write the product as a decimal. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Hard
2.
Prove that (cos 9x - cos 5x)/(sin 17x - sin 3x) = -(sin 2x)/(cos 10x). New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
3.
Write 2 cos 5x cos 3x as a sum of two cosines. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Easy
4.
Prove that (1 - cos 2x + sin 2x)/(1 + cos 2x + sin 2x) = tan x. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
5.
Let θ = 18°, so that 5θ = 90°. Use 2θ = 90° - 3θ to show that sin 18° = (√5 - 1)/4, and give it to… New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Hard
6.
cos x = 0.6. Use the triple-angle formula to find cos 3x. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Easy
7.
cos x = -5/13, and x lies between π/2 and π. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
8.
A and B are acute angles with tan A = 1/2 and tan B = 1/3. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Hard
9.
Prove that tan(π/4 + x) = (1 + tan x)/(1 - tan x). New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
10.
sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
11.
Find the exact value of sin 105°. Then give it to three decimal places. New
High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesStemPy LabStemPy Lab
Easy
12.
How many real solutions does the equation sin x = x/10 have? New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Hard
13.
For y = -2 cos(3x + π), find the amplitude, the period (to 3 decimal places) and the range. New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Medium
14.
The depth of water in a harbour is h = 6 + 2.5 sin (π t)/6 metres, t hours after midnight. New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Medium
15.
Find the period of f(x) = |sin x| + |cos x|. New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Hard
16.
An angle x has sec x < 0 and cot x > 0. In which quadrant does x lie? New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Easy
17.
Find tan 1230°, exactly and as a decimal to 3 places. New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Medium
18.
Find cos(-23π/4) exactly, and as a decimal to 3 places. New
High School (11–12) · Trigonometric Functions and GraphsStemPy LabStemPy Lab
Easy
19.
For which values of x with 0 ≤ x < 2π is sin x = cos x? New
High School (11–12) · Trigonometric Functions and Graphs, Trigonometric IdentitiesStemPy LabStemPy Lab
Hard
20.
An angle x lies between π/2 and π, and tan x = -3/4. Find sin x and cos x. New
High School (11–12) · Trigonometric Functions and Graphs, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
21.
Prove that, wherever both sides are defined: (1 + tan² x) cos² x = 1; (sin x)/(1 + cos x) + (1 +… New
High School (11–12) · Trigonometric Functions and Graphs, Trigonometric IdentitiesStemPy LabStemPy Lab
Medium
22.
The point P on the unit circle at angle x has cos x = -20/29, and P lies below the x-axis. New
High School (11–12) · Trigonometric Functions and Graphs, Trigonometric IdentitiesStemPy LabStemPy Lab
Easy
23.
A motor pulley of radius 4 cm turns at 1500 revolutions per minute. New
High School (11–12) · Angles and Radian MeasureStemPy LabStemPy Lab
Hard
24.
A sprinkler throws water 7.5 m and turns back and forth through 110°. New
High School (11–12) · Angles and Radian MeasureStemPy LabStemPy Lab
Medium
25.
The minute hand of a clock is 9 cm long. New
High School (11–12) · Angles and Radian MeasureStemPy LabStemPy Lab
Medium
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