If cosine theta equals two over three, what are the values of sin θ and tan θ? sine theta equals plus or minus square root of 5 over 3, tangent theta equals negative five over two sine theta equals plus or minus two over nine, tangent theta equals plus or minus square root of five over two sine theta equals plus or minus square root of 5 over 3, tangent theta equals plus or minus square root of 5 over 2 sine theta equals plus or minus two over 9, tangent theta equals negative five over three

Question

Mathematics

Bentley Greene

26 August, 04:37

If cosine theta equals two over three, what are the values of sin θ and tan θ? sine theta equals plus or minus square root of 5 over 3, tangent theta equals negative five over two sine theta equals plus or minus two over nine, tangent theta equals plus or minus square root of five over two sine theta equals plus or minus square root of 5 over 3, tangent theta equals plus or minus square root of 5 over 2 sine theta equals plus or minus two over 9, tangent theta equals negative five over three

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Answers (1)

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Remy · Answer 1

Sin θ = + / -√5/3 and tan θ = + / - √5/2.

Step-by-step explanation:

OK so we have a right triangle in the first quadrant of the unit circle with one angle θ whose cosine is 2/3.

That means that the adjacent side = 2 and the hypotenuse = 3.

So, by Pythagoras, the opposite side = √ (3^2 - 2^2) = + / -√5.

So sin θ = + / -√5/3 and tan θ = + / -√5/2.

* The + / - results from the fact that the triangle may be in the first quadrant or the fourth where the cosine is positive. The sine and tangent are positive in the first quadrant but negative in the fourth.