Let sin(−θ)=−35 and tanθ>0. What is the value of cos(−θ)?

cos(−θ) = -4/5

Step-by-step explanation:

The correct question is as follows;

Let sin(−θ)=−3/5 and tanθ>0. What is the value of cos(−θ)?

Solution as follows

Here in this question, we have that tanθ>0. what this means is that tan is positive here.

Now what do we notice about the value of the sin? For the negative angle to give a negative sin value, what this means is that the value of sin at the particular quadrant is positive, hence we can also conclude that sinθ>0

Now which quadrant do we have both sine and tangent positive? That is only the first quadrant.

Coincidentally, the value of cos here too is positive.

Since we are dealing with the first quadrant, we only need to find the value of theta.

Mathematically;

Sine theta = opposite/hypotenuse

Now ;

Cos theta = adjacent/hypotenuse

So therefore, to find the value of the adjacent , we need to employ the use of Pythagoras’ theorem

Mathematically, the square of the hypotenuse equals the sum of the squares of the adjacent and opposite

According to the values in this question

Adjacent = √(5)^2 -(3^2)

Adjacent = √(16) = 4

Thus ;

cos(−θ) = -4/5

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