write and that is equivalent to each of the following expression,using the related acute angle

a) sin 13pi/6 b) cos 11pi/8
c) tan 7pi/4

a) sin(13π/6)

= sin(2π + π/6)
so we are in quadrant I with an angle of sin π/6
sin π/6 = 1/2

cos(11π/6)
= cos(2π-π/6) .... ( think: 330° = 360° - 30°)
so we are in quad IV and in IV the cosine is positive

= cos π/6 = √3/2

c) tan 7π/4
= tan (2π - π/4) ------ in IV where the tangent is negative
= -tan π/4 = -1

You can and should check your answers with a calculator.

To find the equivalent expression using the related acute angle for each of the given trigonometric expressions, we can use the unit circle and the properties of the trigonometric functions.

Let's go through each expression one by one:

a) sin(13π/6)
First, let's convert 13π/6 into an angle within the range of 0 to 2π (or 0° to 360°). To do this, we divide 13π by 6 and get 2π + π/6. Since 2π makes a full circle and π/6 is an acute angle, we can conclude that sin(13π/6) is equivalent to sin(π/6).
Therefore, an equivalent expression for sin(13π/6) using the related acute angle is sin(π/6).

b) cos(11π/8)
Similarly, let's convert 11π/8 into an angle within the range of 0 to 2π. Dividing 11π by 8 gives us 1π + 3π/8. Since 2π is a full circle and 3π/8 is an acute angle, we can conclude that cos(11π/8) is equivalent to cos(3π/8).
Therefore, an equivalent expression for cos(11π/8) using the related acute angle is cos(3π/8).

c) tan(7π/4)
Once again, let's convert 7π/4 into an angle within the range of 0 to 2π. Dividing 7π by 4 gives us 1π + 3π/4. Since 2π is a full circle and 3π/4 is an acute angle, we can conclude that tan(7π/4) is equivalent to tan(3π/4).
Therefore, an equivalent expression for tan(7π/4) using the related acute angle is tan(3π/4).

In summary:
a) sin(13π/6) = sin(π/6)
b) cos(11π/8) = cos(3π/8)
c) tan(7π/4) = tan(3π/4)