Question

________is an acute angle and sin theta and cos theta are given. Use identities to find tangent theta, cosecant theta, secant theta, and cotangent theta . Where​ necessary, rationalize denominators. sine theta= 12/13, cosine theta= 5/13.

Answer 1

Answer:

tangent theta = 12/5,

cosecant theta = 13/12

secant theta = 13/5

Cotangent theta = 5/12

Step-by-step explanation:

Given sine theta= 12/13, cosine theta= 5/13.

According to SOH CAH TOA

Sintheta = Opposite/Hypotenuse = 12/13

Cosine theta = Adjacent/Hypotenuse = 5/13

Opposite = 12, Adjacent = 5, Hypotenuse = 13

Tan theta = Opposite/Adjacent = 12/5.

cosecant theta = 1/sintheta = 1/{12/13}

cosecant theta = 13/12

secant theta = 1/cos theta = 1/{5/13}

Secant theta = 13/5.

Cotangent theta = 1/tan theta = 1/{12/5} = 5/12