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AssignmentMultiple Choice

Trigonometric Ratios

Question 3 • *CR CCSS Math 2 S2 [M2960OX]

Why are the values for sine and cosine equal at 45°?

Answer
A
All three of the side lengths of the triangle are 1.
B
The length of the side opposite the 45° angle equals 1.
C
The length of the side opposite the 45° angle is twice the length of the side adjacent to the 45° angle.
D
The length of the side opposite the 45° angle equals the length of the side adjacent to the 45° angle.

Explanation

At 45° in a right triangle, the other acute angle is also 45°, so the two legs are equal. The side opposite the 45° angle therefore has the same length as the side adjacent to it. Since sine is opposite ÷ hypotenuse and cosine is adjacent ÷ hypotenuse, the two values are equal. This is choice D.

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