The degree measure of an angle theta is 40 degrees. What is the radian Measure of theta? at what point P does the terminal ray intersect the unit circle (what is the ordered paid P(____, ___)?

180° = π radians , (memorize this relationship)

so 1° = π/180 radians
then 40° = 40(π/180) = ...

To convert the degree measure of an angle to radian measure, we need to use the conversion factor that states π radians is equivalent to 180 degrees.

Given that the degree measure of angle theta is 40 degrees, we can substitute this value into the conversion factor:

θ (in radians) = (θ in degrees) × (π radians / 180 degrees)

θ (in radians) = 40 degrees × (π radians / 180 degrees)

Now, let's simplify this expression:

θ (in radians) = (40 * π) / 180

Simplifying further, we have:

θ (in radians) = π/4

So the radian measure of theta is π/4.

Now, regarding the point P where the terminal ray intersects the unit circle, we know that the terminal ray is the ray that starts from the origin (0, 0) and extends to the point on the unit circle determined by angle theta.

Since the angle theta is in the second quadrant (40 degrees), the x-coordinate of the point P will be negative, while the y-coordinate will be positive.

Using the unit circle reference angles for the second quadrant, we know that the reference angle for 40 degrees will be 180 - 40 = 140 degrees.

Applying the cosine and sine functions, we get:

x-coordinate = cos(140 degrees) = -cos(40 degrees) ≈ -0.766

y-coordinate = sin(140 degrees) = sin(40 degrees) ≈ 0.643

Therefore, the ordered pair P will be P(-0.766, 0.643).