Problem

Use identities to correctly complete the sentence. If $\cos \theta=0.7$ and $\sin \theta=0.5$, then $\tan (-\theta)=$ (Type an integer or decimal rounded to the nearest hundredth as needed.)

Solution

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 \(\sin(-\theta) = -\sin(\theta)\), and the cosine function is even, which means that \(\cos(-\theta) = \cos(\theta)\).

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

Step 4 :Given that \(\cos \theta = 0.7\) and \(\sin \theta = 0.5\), we can substitute these values into the equation.

Step 5 :\(\tan(-\theta) = -\frac{\sin \theta}{\cos \theta} = -\frac{0.5}{0.7} = -0.7142857142857143\)

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

Step 7 :Final Answer: \(\boxed{-0.71}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8446/

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