Match each ratio in the first row with an equivalent ratio from the second row if angle A plus angle B = 90 degrees.
SinA CosA TanA CscA SecA CotA
SinB CosB TanB CscB SecB CotB
Pleaseeee help!!
f(a) = co-f(b) if a+b = 90
that is, cosine(a) = sin(b) if a is complementary to b
So,
sinA = cosB
tanA = cotB
secA = cscB
etc.
To match each ratio in the first row with an equivalent ratio from the second row, we need to understand the trigonometric functions and their relationships.
1. Sine (Sin) is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, SinA = opposite/hypotenuse.
2. Cosine (Cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. So, CosA = adjacent/hypotenuse.
3. Tangent (Tan) is the ratio of the length of the opposite side to the length of the adjacent side. So, TanA = opposite/adjacent.
4. Cosecant (Csc) is the reciprocal of the sine function. So, CscA = 1/SinA.
5. Secant (Sec) is the reciprocal of the cosine function. So, SecA = 1/CosA.
6. Cotangent (Cot) is the reciprocal of the tangent function. So, CotA = 1/TanA.
Now, since A + B = 90 degrees, it means that angle A and angle B are complementary angles. This means that the sine, cosine, and tangent functions for A are the same as the complementary angles for B.
So, the equivalent ratios for each ratio in the first row are:
SinA = CosB
CosA = SinB
TanA = CotB
CscA = SecB
SecA = CscB
CotA = TanB
By matching these equivalent ratios from the first row to the second row, you can successfully complete the matching exercise.