Trigonometric Identities & Equations — Drills
Trigonometric Identities & Equations has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
- Isolate — Get the variable alone on one side.
- Identity — An equation true for every value, like 2(x + 3) = 2x + 6.
- Sine — sin θ = oppositehypotenuse.
- Cosine — cos θ = adjacenthypotenuse.
- Secant — A line that cuts the circle at two points.
- Reference angle — The acute angle between the terminal side and the x-axis.
- Pythagorean identity — sin2θ + cos2θ = 1.
- y-coordinate — The second number — how far up or down.
- Quadrant — One of the four regions the axes divide the plane into.
Identity
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If cosθ=513 and θ is acute, find sinθ.
Worked answer
12/13
sin2θ = 1-25169 = 144169
Acute means positive: 1213
Problem 2
If cosθ=1517 and θ is acute, find sinθ.
Worked answer
8/17
sin2θ = 1-225289 = 64289
Acute means positive: 817
Quadrants
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If sinθ=513 and θ is in quadrant II, find cosθ.
Worked answer
-12/13
cos2θ=1-25169=144169
Quadrant II has x negative
Problem 2
If sinθ=817 and θ is in quadrant II, find cosθ.
Worked answer
-15/17
cos2θ=1-64289=225289
Quadrant II has x negative
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve sinθ=√32 for 0° ≤ θ < 360°. Give both answers, smallest first.
Worked answer
60,120
Reference angle 60°
60° and 180-60=120°
Problem 2
Solve sinθ=√22 for 0° ≤ θ < 360°. Give both answers, smallest first.
Worked answer
45,135
Reference angle 45°
45° and 180-45=135°
Solvecos
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve cosθ=cos 45° for 0° ≤ θ < 360°, θ ≠ 45°. Give the other answer.
Worked answer
315
360-45=315
Problem 2
Solve cosθ=cos 30° for 0° ≤ θ < 360°, θ ≠ 30°. Give the other answer.
Worked answer
330
360-30=330
Reciprocal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If sinθ=18, find cscθ.
Worked answer
8
11/8=8
Problem 2
If sinθ=12, find cscθ.
Worked answer
2
11/2=2
Tan
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If sinθ=45 and cosθ=35, find tanθ.
Worked answer
4/3
4/53/5 = 43
Problem 2
If sinθ=513 and cosθ=1213, find tanθ.
Worked answer
5/12
5/1312/13 = 512