can you correct the rest for me please?

Express each as a function of theta:

a. sin (270deg + theta)= cos theta
b. cos (pi + theta)= -cos theta
c. tan (810 + theta)= ?????
d. sin (theta - 180)= -sin theta

a. To express sin(270° + θ) as a function of θ, we can use the property sin(x + 270°) = cos(x). Therefore, sin(270° + θ) = cos(θ).

b. To express cos(π + θ) as a function of θ, we can use the property cos(x + π) = -cos(x). Therefore, cos(π + θ) = -cos(θ).

c. To express tan(810° + θ) as a function of θ, we can use the property tan(x + n*180°) = tan(x), where n is an integer. Therefore, tan(810° + θ) = tan(θ).

d. To express sin(θ - 180°) as a function of θ, we can use the property sin(x - 180°) = -sin(x). Therefore, sin(θ - 180°) = -sin(θ).

Sure! I'd be happy to help correct the rest for you.

a. To express sin(270° + theta) as a function of theta, we can use the identity sin(x + 270°) = cos(x). Therefore, sin(270° + theta) = cos(theta).

b. To express cos(pi + theta) as a function of theta, we can use the identity cos(x + pi) = -cos(x). Therefore, cos(pi + theta) = -cos(theta).

c. To express tan(810° + theta) as a function of theta, we can use the periodicity of the tangent function. Since a full circle is 360°, we can subtract multiples of 360° from the given angle to express it as an equivalent angle within one full circle. In this case: 810° + theta = 2(360°) + 90° + theta = 90° + theta. Therefore, tan(810° + theta) = tan(90° + theta).

d. To express sin(theta - 180°) as a function of theta, we can use the identity sin(x - 180°) = -sin(x). Therefore, sin(theta - 180°) = -sin(theta).

So, the corrected expressions are:
a. sin(270° + theta) = cos(theta)
b. cos(pi + theta) = -cos(theta)
c. tan(810° + theta) = tan(90° + theta)
d. sin(theta - 180°) = -sin(theta)