Question

100 POINTS AND BRAINLIEST!! PRE CALC

Answer 1

Answer:

b

Step-by-step explanation:

sin x = $\frac{opposite}{hypotenuse}$ = $\frac{3}{5}$

This is a 3- 4- 5 right triangle

with adjacent side = 4 , then

cos x = $\frac{adjacent}{hypotenuse}$ = $\frac{4}{5}$ , thus

tan x = $\frac{sinx}{cosx}$ = $\frac{\frac{3}{5} }{\frac{4}{5} }$ = $\frac{3}{5}$ × $\frac{5}{4}$ = $\frac{3}{4}$

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sin y = $\frac{7}{25}$

This is a 7- 24- 25 right triangle

with adjacent side = 24 , then

cos y = $\frac{adjacent}{hypotenuse}$ = $\frac{24}{25}$ , thus

tan y = $\frac{siny}{cosy}$ = $\frac{\frac{7}{25} }{\frac{24}{25} }$ = $\frac{7}{25}$ × $\frac{25}{24}$ = $\frac{7}{24}$

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tan(x - y) = $\frac{tanx-tany}{1+tanxtany}$

             = $\frac{\frac{3}{4}-\frac{7}{24} }{1+\frac{3}{4}(\frac{7}{24}) }$

             = $\frac{\frac{11}{24} }{1+\frac{21}{96} }$

             = $\frac{\frac{11}{24} }{\frac{117}{96} }$

             = $\frac{11}{24}$ × $\frac{96}{117}$

             = $\frac{11}{1}$ × $\frac{4}{117}$

             = $\frac{44}{117}$ → b

Answer 2

Answer:

B

Step-by-step explanation:

sinx = 3/5

to find the value of x...figure sine inverse(Arcsin) of 3/5 out.

sin^-1 ( 3/5) = 0.64.

siny = 7/25

sin^-1(7/25) = 0.28

x = 0.64

y = 0.28

tan(x-y)

=tan(0.64-0.28)

= tan (0.36)

= tan (9/25)

= 0.376.

now divide every fraction given from a - d to find the one equivalent to 0.376 because that's the value of tan(x-y).

B. 44 / 117 = 0.376.