#Sin theta = cos theta# is possible, where #theta# is an angle in a triangle. Is this true or false?

2 Answers
May 25, 2016

This is true. See below for proof.

Explanation:

Consider the classic #45˚, 45˚, 90˚ # triangle, as shown in the following diagram.

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The definition of #sin# is opposite/hypotenuse.

The definition of #cos# is adjacent/hypotenuse.

In the vast majority of situations, the side adjacent #theta# will be different than the side opposite #theta#. However, in the extremely particular case that the opposite and adjacent sides are the same, #sintheta# and #costheta# will be equal, because these functions measure the relationships between sides, and if these relationships are equal, the functions will be equal in value.

Hopefully this helps!

May 25, 2016

True.

Explanation:

If sin x = cos x, then tan x = 1 --> x = pi/4.
The answer is true, when a right triangle has 2 angles of (pi/4)