Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and side is 4.

The triangle is missing, so i have attached it.

1)sin(α) = 4/7

2)cos(β) = 4/7

3)tan(α) = 4/√33

4)cot(β) = 4/√33

5)sec(α) = 7/√33

6)csc(β) = 7/√33

Step-by-step explanation:

(1) sin(α)

From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.

Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7

2) cos(β)

Cosine of an angle = adjacent side/hypotenuse.

In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7

3)tan(α)

tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.

Using the pythagoras theorem,

Adjacent side = √(7² - 4²)

Adjacent side = √(49 - 16)

Adjacent side = √33.

Thus, tan(α) = 4/√33

4) cot(β)

cot of an angle is the reciprocal of tangent of same angle.

The adjacent side to β is 4 while the opposite is √33.

So, tan(β) = (√33)/4

cot(β) = 1/tan(β)

cot(β) = 1/[(√33)/4]

cot(β) = 4/√33

5)sec(α)

sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.

Thus, sec(α) = 1/cosα = 7/√33.

6) csc(β)

Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.

Thus, csc(β) = 1/sin(β) = 7/√33

Ithink your answer is c hope that

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )