Sine and Cosine

Geometry Level 1

If $\sin(x)+\cos(y)=2$ , determine the value of $x+y$ in degrees, for $0^\circ \le x \le 360^\circ$ and $0^\circ \le y < 360^\circ$ .

The answer is 90.

1 solution

Yashas Ravi
Mar 22, 2019

Since the maximum value of $\sin(a)$ or $\cos(a)$ for any real $a$ is $1$ , then the maximum value of $\sin(x)$ and $\cos(y)$ are both $1$ . As a result, the maximum value of $\sin(x)+\cos(y)=2$ . This only happens when $x=90$ and $y=0$ , since $\sin(90)=1$ and $\cos(0)=1$ . As a result, $(x+y)=0+90=90$ .

Sine and Cosine

The answer is 90.

1 solution

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