Answer:
a. 4/5
b. 3/5
c.3/5
d.4/5
Step-by-step explanation:
Here, we are to use the shape to calculate the sine and cosine in the question.
We should understand that, the sine of an angle is the ratio of the opposite to the hypotenuse while the cos of an angle refers to the ratio of the adjacent to the hypotenuse.
The hypotenuse is the longest side in the right angle triangle. It is the side that faces the angle 90. The opposite refers to the side that faces the angle we are considering while the adjacent is the other side of the triangle.
When considering angle D, our opposite is 12 and adjacent is 9
when considering angle E, our opposite is 9 and adjacent is 12.
The hypotenuse in each of the cases is the longest side in the triangle which is the side facing F, 15.
Sin D = opposite/hypotenuse = 12/15 = 4/5
Sin E = opposite/hypotenuse = 9/15 = 3/5
Cos D = adjacent/hypotenuse = 9/15 = 3/5
Cos E = adjacent/hypotenuse = 12/15 = 4/5
The value of sin D, sin E , cos D , and cos E in simplest fraction form are as follows:
Sin D = 4 / 5
sin E = 3 / 5
cos D = 3 / 5
cos E = 4 / 5
The simplest trigonometric ratios expression are as follows:
Therefore,
Sin D = opposite / hypotenuse = 12 / 15 = 4 / 5
sin E = opposite / hypotenuse = 9 / 15 = 3 / 5
cos D = adjacent / hypotenuse = 9 / 15 = 3 / 5
cos E = adjacent / hypotenuse = 12 / 15 = 4 / 5
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