Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct--if you don't, review that part of the lesson.
Which expression is equal to \( \frac{1 + \sin x}{\cos x} \) using identities?
- \( \sec x + \tan x \)
- \( \sec x + \cot x \)
- \( \csc x + \tan x \)
- \( \csc x + \cot x \)
The expression can be separated into two parts and rewritten with the reciprocal and quotient identities.
This is not the correct relationship for the second part of the expression.
This is not the correct relationship for the first part of the expression.
This is not the correct relationship for both parts of the expression.
Which expression is equal to \( \cos^{2} x - \sin^{2} x \) using identities?
- \( 1 + 2\sin^{2} x \)
- \( \sin^{2} x + 1 \)
- \( 1 - \cos^{2} x \)
- \( 2\cos^{2} x - 1 \)
This is not the correct relationship for the expression. Use the Pythagorean identity and simplify.
This is not the correct relationship for the expression. Use the Pythagorean identity and simplify.
This is not the correct relationship for the expression. Use the Pythagorean identity and simplify.
The expression is equivalent by using the Pythagorean identity and simplifying.
Which is equal to \( \left( \sin x + \cos x \right)^{2} + (\sin x - {\cos x)}^{2} \) using identities?
- \( - \)2
- \( - \)1
- 1
- 2
This value is a result of not simplifying correctly.
This value is a result of not simplifying correctly.
This value is a result of not simplifying correctly.
The expression is equivalent by using multiplication, combining like terms, and Pythagorean identities.
Which expression is equal to \( \frac{\tan x}{\sec x} + \frac{\cot x}{\csc x} \) using identities?
- \( \sin x - \cos x \)
- \( \sin x + \cos x \)
- \( \tan x - \cot x \)
- \( \tan x + \cot x \)
The expression is not simplified correctly.
The expression is equivalent by rewriting the expression using sines and cosines.
The expression was not rewritten correctly. Rewrite the expression using sines and cosines.
The expression was not rewritten correctly. Rewrite the expression using sines and cosines.
Summary
Questions answered correctly:
Questions answered incorrectly: