Question

Given sin a equals 21/29 and the angle a is in quadrant one find the exact value of code AN simplest radical form using a rational denominator

Answer 1

To find cos a from sin a = 21/29 where angle a is in quadrant one, use the Pythagorean identity to get cos a = 20/29 in simplest radical form with a rational denominator.

Step-by-step explanation:

The student has given that sin a = 21/29 and has asked to find the exact value of cos a in simplest radical form with a rational denominator, given that angle a is in quadrant one. Since we know the sin a, we can use the Pythagorean identity sin² a + cos² a = 1 to find cos a. This identity implies that cos² a = 1 - sin² a.

First, we calculate sin² a:

• sin² a = (21/29)²

Next, we calculate cos² a:

• cos² a = 1 - sin² a
• cos² a = 1 - (21/29)²
• cos² a = 1 - (441/841)
• cos² a = (841/841) - (441/841)
• cos² a = (400/841)

Since angle a is in quadrant one, cos a is positive, so:

• cos a = √(400/841)
• cos a = 20/29

The answer in simplest radical form with a rational denominator is cos a = 20/29.

Answer 2

To find cos a from sin a = 21/29 where angle a is in quadrant one, use the Pythagorean identity to get cos a = 20/29 in simplest radical form with a rational denominator.

Step-by-step explanation:

The student has given that sin a = 21/29 and has asked to find the exact value of cos a in simplest radical form with a rational denominator, given that angle a is in quadrant one. Since we know the sin a, we can use the Pythagorean identity sin² a + cos² a = 1 to find cos a. This identity implies that cos² a = 1 - sin² a.

First, we calculate sin² a:

• sin² a = (21/29)²

Next, we calculate cos² a:

• cos² a = 1 - sin² a
• cos² a = 1 - (21/29)²
• cos² a = 1 - (441/841)
• cos² a = (841/841) - (441/841)
• cos² a = (400/841)

Since angle a is in quadrant one, cos a is positive, so:

• cos a = √(400/841)
• cos a = 20/29

The answer in simplest radical form with a rational denominator is cos a = 20/29.