Question

If tan theta = 3/4
find the values of sin 2theta, cos 2theta and tan 2theta​

Answer 1

The answer is

1)0.96 to 2d.p

2)0.28 to 2d.p

3)3.49 to 2d.p

Step-by-step explanation:

tan0=3/4

0=tan‐¹[3/4]

0=36.9°

0≈37°

1) sin2(0)

sin (2×37)=sin 74=0.96 to 2.dp

2)cos 2(37)

sin(2×37)=cos 74=0.28 to 2d.p

3) tan20

=tan(2×37)=tan74=3.49 to 2d.p

Answer 2

Given tan(theta) = 3/4, we find sin(2theta) = 24/25, cos(2theta) = 7/25, and tan(2theta) = 24/7 using the double angle formulas for sine, cosine, and tangent.

Step-by-step explanation:

If tan(theta) = 3/4, we can start by finding the values of sin(theta) and cos(theta) using trigonometric identities. Knowing the value of tan(theta), we can think of a right-angled triangle where the opposite side is 3 and the adjacent side is 4, giving us a hypotenuse of √(3² + 4²) = 5 using the Pythagorean theorem. Hence, sin(theta) = 3/5 and cos(theta) = 4/5.

We will employ the double angle formulas to find sin(2theta), cos(2theta), and tan(2theta):

sin(2theta) = 2sin(theta)cos(theta) = 2*(3/5)*(4/5) = 24/25

cos(2theta) = cos²(theta) - sin²(theta) = (4/5)² - (3/5)² = 7/25

tan(2theta) = sin(2theta) / cos(2theta) = (24/25) / (7/25) = 24/7