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Questions and Answers
Which trigonometric function is equal to 0.4?
Which trigonometric function is equal to 0.4?
Without using a calculator, what is the value of $cos(765)$?
Without using a calculator, what is the value of $cos(765)$?
Without using a calculator, find the value of $x$ if $4^x = 16$
Without using a calculator, find the value of $x$ if $4^x = 16$
Prove that $tan(A + B) = \frac{tan(A) + tan(B)},{1 - tan(A)tan(B)}$
Prove that $tan(A + B) = \frac{tan(A) + tan(B)},{1 - tan(A)tan(B)}$
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Study Notes
Trigonometric Functions
- The sine of an angle in a right triangle is equal to the ratio of the opposite side to the hypotenuse.
- The cosine of an angle in a right triangle is equal to the ratio of the adjacent side to the hypotenuse.
Trigonometric Identities
- The cosine of an angle is equal to the cosine of the angle's reference angle.
- The cosine of an angle that is a multiple of 360 degrees is equal to the cosine of the angle's reference angle.
Exponential Functions
- If a is a positive real number and a ≠ 1, then a^x = y is equivalent to loga(y) = x.
- In this case, 4^x = 16 is equivalent to log4(16) = x.
Proofs
- To prove the tangent angle sum identity, tan(A + B) = tan(A) + tan(B) / 1 - tan(A)tan(B), we can use the following steps:
- Start with the formulas for sin(A + B) and cos(A + B)
- Substitute the formulas for sin(A + B) and cos(A + B) into the formula for tan(A + B)
- Simplify the resulting expression to get the desired identity
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Description
This quiz tests your trigonometry skills by challenging you to solve various trigonometric equations and prove trigonometric identities. Practice finding the value of sin and cos without using a calculator, as well as solving for unknown variables and evaluating expressions.
