Trigonometry Midterm Exam
A free Trigonometry lesson from the “Graphs of Trig Functions” unit, with a worked example and practice problems including step-by-step solutions.
The midterm reviews right-triangle trig, angle measure, unit-circle values, and graph features before the identity and equation units.
What you'll learn
- Solve non-right triangles with Law of Sines and Law of Cosines
- Use trig area, vectors, and periodic models
- Choose a method from mixed applied information
Worked example
Problem. Trigonometry Midterm Exam: If sin(theta)=3/5 and theta is in Quadrant I, find cos(theta).
- Use sin^2 + cos^2 = 1.
- cos^2 = 16/25.
- Cosine is positive, so cos = 4/5.
Answer: 4/5
Practice problems
1. Trigonometry Midterm Exam: Convert 45 degrees to radians.
Show solution
- Midterm Exam Review: First identify exactly what the question is asking: Trigonometry Midterm Exam: Convert 45 degrees to radians.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Use 180 degrees = pi radians.
- Compute 45 * pi/180.
- The result is pi/4.
- Check the result by substituting or estimating: the response should match pi/4 and make sense in the original problem.
Answer: pi/4
2. Trigonometry Midterm Exam: Evaluate sin(7pi/6).
Show solution
- Midterm Exam Review: First identify exactly what the question is asking: Trigonometry Midterm Exam: Evaluate sin(7pi/6).
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Sine is the y-coordinate.
- Use the point (-sqrt(3)/2, -1/2).
- sin(7pi/6) = -1/2.
- Check the result by substituting or estimating: the response should match -1/2 and make sense in the original problem.
Answer: -1/2
3. Trigonometry Midterm Exam: Find the period of y = sin(4x).
Show solution
- Midterm Exam Review: First identify exactly what the question is asking: Trigonometry Midterm Exam: Find the period of y = sin(4x).
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- For sine, period = 2pi/|b|.
- Here b = 4.
- The period is pi/2.
- Check the result by substituting or estimating: the response should match pi/2 and make sense in the original problem.
Answer: pi/2
4. Trigonometry Midterm Exam: If sin(theta)=3/5 and theta is in Quadrant I, find cos(theta).
Show solution
- Midterm Exam Review: First identify exactly what the question is asking: Trigonometry Midterm Exam: If sin(theta)=3/5 and theta is in Quadrant I, find cos(theta).
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Use sin^2 + cos^2 = 1.
- cos^2 = 16/25.
- Cosine is positive, so cos = 4/5.
- Check the result by substituting or estimating: the response should match 4/5 and make sense in the original problem.
Answer: 4/5
5. Trigonometry Midterm Exam: Write the general solution to tan(x) = 1.
Show solution
- Midterm Exam Review: First identify exactly what the question is asking: Trigonometry Midterm Exam: Write the general solution to tan(x) = 1.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- tan(pi/4)=1.
- Tangent has period pi.
- Add pi*k.
- Check the result by substituting or estimating: the response should match x = pi/4 + pi*k and make sense in the original problem.
Answer: x = pi/4 + pi*k
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