Evaluating with standard angle values: Class 10 practice
The ratios of 0°, 30°, 45°, 60° and 90° are exact: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, tan 45° = 1, and cos θ = sin(90° − θ).. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Surds
The idea behind evaluating with standard angle values
The ratios of 0°, 30°, 45°, 60° and 90° are exact: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, tan 45° = 1, and cos θ = sin(90° − θ).
Step-by-step method
- Replace each ratio by its exact value.
- Simplify the arithmetic carefully.
- Rationalise if needed.
Worked example 1 (Basic)
Evaluate 5sin 60° × sin 60°.
- sin 60° = 0.8660…, sin 60° = 0.8660…
- = 15/4
- Answer: 15/4
Worked example 2 (Standard)
Evaluate 2tan 45° + sin 90°.
- tan 45° = 1.0000…, sin 90° = 1.0000…
- = 3
- Answer: 3
Worked example 3 (Challenge)
Evaluate 4sin 30° + cos 60°.
- sin 30° = 0.5000…, cos 60° = 0.5000…
- = 5/2
- Answer: 5/2
Common mistakes and misconceptions
- Mixing up sin 30° and sin 60°
- Saying tan 90° = 1
Practice questions
- (Basic) Evaluate 2sin 90° + cos 90°.
- (Basic) Evaluate tan 45° + sin 90°.
- (Standard) Evaluate 3tan 60° × tan 30°.
- (Standard) Evaluate 3cos 0° − sin 30°.
- (Challenge) Evaluate cos 0° − sin 30°.
- (Challenge) Evaluate 5cos 0° − sin 30°.
Answer key with full working
- Q1: sin 90° = 1.0000…, cos 90° = 0.0000… → = 2 → Answer: 2
- Q2: tan 45° = 1.0000…, sin 90° = 1.0000… → = 2 → Answer: 2
- Q3: tan 60° = 1.7321…, tan 30° = 0.5774… → = 3 → Answer: 3
- Q4: cos 0° = 1.0000…, sin 30° = 0.5000… → = 5/2 → Answer: 5/2
- Q5: cos 0° = 1.0000…, sin 30° = 0.5000… → = 1/2 → Answer: 1/2
- Q6: cos 0° = 1.0000…, sin 30° = 0.5000… → = 9/2 → Answer: 9/2
Syllabus note
This skill is listed under "Trigonometry" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is evaluating with standard angle values in?
"Trigonometry", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.