Given that sin theta=5/7 and theta is acute. Find without using the table value of cos theta
the other side of the triangle is √(7^2-5^2) = √24
now use that to evaluate the cosine
To find the value of cos(theta) using the given information, you can apply the Pythagorean identity along with the given value of sin(theta).
The Pythagorean identity states that sin^2(theta) + cos^2(theta) = 1.
Now, we can start solving for cos(theta):
1. Start with the Pythagorean identity: sin^2(theta) + cos^2(theta) = 1.
2. Substitute the given value of sin(theta): (5/7)^2 + cos^2(theta) = 1.
3. Simplify the equation: 25/49 + cos^2(theta) = 1.
4. Subtract 25/49 from both sides of the equation: cos^2(theta) = 1 - 25/49.
5. Simplify the equation further: cos^2(theta) = (49-25)/49.
6. Calculate the value inside the parentheses: cos^2(theta) = 24/49.
7. Take the square root of both sides to find cos(theta). Since theta is acute, cos(theta) is positive: cos(theta) = sqrt(24/49).
8. Simplify the square root: cos(theta) = sqrt(24)/sqrt(49).
9. Further simplify sqrt(49) to get the final answer: cos(theta) = sqrt(24)/7.
Therefore, the value of cos(theta) is sqrt(24)/7.