Trigonometry ratio. Evaluate the following and show your workings. A. sin 103° B.cos 113° C.sin 136° D.cos 157°
A. To evaluate sin 103°, we first need to determine which quadrant 103° is in. Since 90° < 103° < 180°, we know it is in the second quadrant. In that quadrant, sine is positive, so we know the answer will be positive.
We can use the sine function on our calculator or reference sheet to find that sin 103° = 0.973.
B. To evaluate cos 113°, we first need to determine which quadrant 113° is in. Since 90° < 113° < 180°, we know it is in the second quadrant. In that quadrant, cosine is negative, so we know the answer will be negative.
We can use the cosine function on our calculator or reference sheet to find that cos 113° = -0.321.
C. To evaluate sin 136°, we first need to determine which quadrant 136° is in. Since 90° < 136° < 180°, we know it is in the second quadrant. In that quadrant, sine is positive, so we know the answer will be positive.
We can use the sine function on our calculator or reference sheet to find that sin 136° = 0.469.
D. To evaluate cos 157°, we first need to determine which quadrant 157° is in. Since 90° < 157° < 180°, we know it is in the second quadrant. In that quadrant, cosine is negative, so we know the answer will be negative.
We can use the cosine function on our calculator or reference sheet to find that cos 157° = -0.985.
A. To evaluate sin 103°, you can use the unit circle or a calculator.
Using the unit circle:
Step 1: Draw a unit circle.
Step 2: Locate the angle 103° on the circle.
Step 3: Find the y-coordinate of the point where the angle intersects the unit circle. This is the sine of the angle.
Step 4: So, sin 103° = approximately 0.938.
Using a calculator:
Step 1: Open a calculator and set it to degree mode.
Step 2: Enter "sin(103)" in the calculator.
Step 3: Press the calculate or equal button.
Step 4: The result is approximately 0.938.
Therefore, sin 103° = 0.938.
B. To evaluate cos 113°, you can use the unit circle or a calculator.
Using the unit circle:
Step 1: Draw a unit circle.
Step 2: Locate the angle 113° on the circle.
Step 3: Find the x-coordinate of the point where the angle intersects the unit circle. This is the cosine of the angle.
Step 4: So, cos 113° = approximately -0.612.
Using a calculator:
Step 1: Open a calculator and set it to degree mode.
Step 2: Enter "cos(113)" in the calculator.
Step 3: Press the calculate or equal button.
Step 4: The result is approximately -0.612.
Therefore, cos 113° = -0.612.
C. To evaluate sin 136°, you can use the unit circle or a calculator.
Using the unit circle:
Step 1: Draw a unit circle.
Step 2: Locate the angle 136° on the circle.
Step 3: Find the y-coordinate of the point where the angle intersects the unit circle. This is the sine of the angle.
Step 4: So, sin 136° = approximately 0.970.
Using a calculator:
Step 1: Open a calculator and set it to degree mode.
Step 2: Enter "sin(136)" in the calculator.
Step 3: Press the calculate or equal button.
Step 4: The result is approximately 0.970.
Therefore, sin 136° = 0.970.
D. To evaluate cos 157°, you can use the unit circle or a calculator.
Using the unit circle:
Step 1: Draw a unit circle.
Step 2: Locate the angle 157° on the circle.
Step 3: Find the x-coordinate of the point where the angle intersects the unit circle. This is the cosine of the angle.
Step 4: So, cos 157° = approximately -0.988.
Using a calculator:
Step 1: Open a calculator and set it to degree mode.
Step 2: Enter "cos(157)" in the calculator.
Step 3: Press the calculate or equal button.
Step 4: The result is approximately -0.988.
Therefore, cos 157° = -0.988.