θ is an angle in standard position that terminates in Quadrant II. If sinθ =2/3 , then cos2θ = _____.
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<u>Given</u>:
The triangle ABC is a right triangle.
The length of AC = 25, the length of AB = 7 and the length of BC = 24
We need to determine the ratios of sin C, cos C and tan C.
<u>Ratio of sin C:</u>
Using the trigonometric ratio, the ratio of sin C is given by
where and
Thus, we get;
Substituting the values, we get;
Thus, the ratio of sin C is
<u>Ratio of cos C:</u>
The ratio of cos C can be determined using the trigonometric ratio.
Thus, we have;
where and
Substituting the values, we get;
Thus, the ratio of cos C is
<u>Ratio of tan C:</u>
The ratio of tan C can be determined using the trigonometric ratio.
Thus, we have;
where and
Thus, we have;
Substituting the values, we get;
Thus, the ratio of tan C is