A) P is approximately (0.883, 0.469), is a point on the unit circle with angle 28 degrees estimate the following.
Sin 152 degrees =
Cos 152 degrees =
please help me step by step
To estimate the values of sin 152 degrees and cos 152 degrees, we can use the following steps:
Step 1: Convert the given angle of 152 degrees to the equivalent angle on the unit circle.
To do this, we need to subtract multiples of 360 degrees from the given angle until we obtain an angle within the range of 0 to 360 degrees.
152 degrees - 360 degrees = -208 degrees (outside the range)
152 degrees - 360 degrees = -208 degrees (still outside the range)
152 degrees - 360 degrees = -208 degrees (still outside the range)
152 degrees - 360 degrees = -208 degrees (still outside the range)
Now we have an angle within the range: 152 degrees - 4 * 360 degrees = -208 degrees.
Step 2: Convert the angle to positive by adding 360 degrees.
-208 degrees + 360 degrees = 152 degrees
So, sin 152 degrees and cos 152 degrees can be approximated by finding the values at the angle 152 degrees.
Step 3: Use the values from the unit circle to estimate sin 152 degrees and cos 152 degrees.
Looking at the unit circle, we find the point P with coordinates (0.883, 0.469) that corresponds to the angle of 28 degrees.
Since both 152 degrees and 28 degrees belong to the same reference angle when measured from the positive x-axis, the values for sine and cosine will be the same but with different signs based on the quadrant.
For sin 152 degrees:
Since P is in the first quadrant (where both x and y values are positive), the value of sin 152 degrees is positive.
Therefore, sin 152 degrees ≈ sin 28 degrees ≈ 0.469.
For cos 152 degrees:
Since P is in the first quadrant (where both x and y values are positive), the value of cos 152 degrees is positive.
Therefore, cos 152 degrees ≈ cos 28 degrees ≈ 0.883.
Hence, the estimations are:
sin 152 degrees ≈ 0.469
cos 152 degrees ≈ 0.883