Question

Find the value of r that will make the equation sin 73 cos ° = r true when 0 90 °< < ° r . explain your answer.

Answer 1

The sine of an angle is equal to the cosine of the complementary angle. 
That is; sin r = cos 90 -r , where r is an acute angle
Therefore; 
sin 73 = cos (90-73)
sin 73 = cos 17
Hence the value of r = 17

Answer 2

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of r is 17°.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

As we know that the value of the sine angle is equal to the value of the cosine of its complementary angle. Therefore, we can write,

$Sin(x) = Cos(90-x)$

Now, as it is given that the value of Sin(73°)=Cos(r), where the value of r is between 0° to 90°. Therefore, we can write,

$\rm Sin(73^o )= Cos(r) = Cos(90^o-73^o)\\\\Sin(73^o) = Cos(r)=Cos(17^o)$

Hence, the value of r is 17°.

Learn more about Trigonometric functions:

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