Trigonometric Identities Practice 1: Core Identities

Practise focused skills from Trigonometric Identities

MathematicsGrade 10Mixed10 questions20 min

Print / Save as PDF

Preview

Preview questions

Sample preview - start assignment to submit answers.

Focus question style

Section A: Identity Foundations · 5 questionsSection B: Simplify and Check · 5 questions

Preview onlyStart free practice to answer.

Section A: Identity Foundations

Distinguish identities and derive core identities.

Choose the best answer for each question.

Question 1

EasyQuestion

Which statement best describes a trigonometric identity?

Topic: Identity Basics · Skill: Distinguish equation and identity

Question 2

MediumQuestion

Which is an identity rather than an equation to solve for one value?

Topic: Identity Basics · Skill: Distinguish equation and identity

Question 3

MediumQuestion

In a right triangle, if $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$ , which theorem leads to $\sin^2A+\cos^2A=1$ ?

Topic: Pythagorean Identity · Skill: Prove sin²A + cos²A = 1

Question 4

MediumQuestion

If $\sin A=\frac{3}{5}$ for acute $A$ , what is $\cos A$ ?

Topic: Pythagorean Identity · Skill: Use sin²A + cos²A = 1

Question 5

AdvancedQuestion

If $\cos A=\frac{12}{13}$ for acute $A$ , find $\sin A$ .

Topic: Pythagorean Identity · Skill: Use sin²A + cos²A = 1

What this assignment covers

Understand identities and use the main Pythagorean identities.

Skills and sections

Distinguish equation and identity, Prove sin²A + cos²A = 1, Use sin²A + cos²A = 1, Derive 1 + tan²A = sec²A, Derive 1 + cot²A = cosec²A

Section A: Identity Foundations: 5 questions
Section B: Simplify and Check: 5 questions