If cos (A) =0.95 and sin (B)=0.95, what can be said about A and B?
If they are in QI, they are complementary.
That's what the co in cosine means -- sine of the complement
To determine what can be said about A and B given that cos(A) = 0.95 and sin(B) = 0.95, we can use trigonometric identities and properties.
1. For A: Since cos(A) = 0.95, we can use the inverse cosine function (arccos) to find the value of A. Taking the inverse cosine of both sides:
A = arccos(0.95)
We can evaluate this using a calculator, which gives us:
A ≈ 18.19°
Therefore, we can say that A is approximately equal to 18.19 degrees.
2. For B: Similarly, since sin(B) = 0.95, we can use the inverse sine function (arcsin) to find the value of B. Taking the inverse sine of both sides:
B = arcsin(0.95)
Evaluating this using a calculator:
B ≈ 69.47°
Thus, we can say that B is approximately equal to 69.47 degrees.
In summary, given cos(A) = 0.95 and sin(B) = 0.95, we can determine that A is approximately 18.19 degrees and B is approximately 69.47 degrees.
To determine what can be said about angles A and B given the information that cos(A) = 0.95 and sin(B) = 0.95, we need to consider the properties of trigonometric functions.
First, let's look at the value of cos(A) = 0.95. The cosine function gives the ratio of the adjacent side to the hypotenuse in a right-angle triangle. Since the range of cosine is between -1 and 1, we can conclude that angle A is an acute angle.
Next, consider the value of sin(B) = 0.95. The sine function gives the ratio of the opposite side to the hypotenuse in a right-angle triangle. Similar to cosine, the range of sine is also between -1 and 1. Thus, we can deduce that angle B is also an acute angle.
Considering the values of cos(A) = 0.95 and sin(B) = 0.95, we can conclude that both angles A and B are acute angles.