Problem

Use identities to correctly complete the sentence.
If cosθ=0.7 and sinθ=0.5, then tan(θ)=
(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer

Expert–verified
Hide Steps
Answer

Final Answer: 0.71

Steps

Step 1 :The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle. In this case, we are asked to find the tangent of the negative of the angle.

Step 2 :The sine function is odd, which means that sin(θ)=sin(θ), and the cosine function is even, which means that cos(θ)=cos(θ).

Step 3 :Therefore, we can find tan(θ) by taking the negative of the ratio of the sine to the cosine.

Step 4 :Given that cosθ=0.7 and sinθ=0.5, we can substitute these values into the equation.

Step 5 :tan(θ)=sinθcosθ=0.50.7=0.7142857142857143

Step 6 :Rounding to the nearest hundredth, we get tan(θ)=0.71

Step 7 :Final Answer: 0.71

link_gpt