If sin theta = 2/3 which is possible
1 answer:
Answer:
<h2>C. cos theta = √5/3 and tan theta = 2/√5</h2><h2>D. sec theta = 3/√5 and tan theta = 2/√5</h2>Step-by-step explanation:
According to SOH in SOH, CAH TOA;
SOH means sin theta = opposite/hypotenuse = 2/3
This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.
According to Pythagoras theorem; hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 2²
adj² = 9 - 4
adj² = 5
adj = √5
Hence the adjacent side is √5.
From the trigonometry identity above;
cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5
Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)
sec theta = hyp/adj = 3/√5
<em>From the above calculation, the following are possible:</em>
<em>cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5</em>
<em></em>
The correct options are C and D
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