refer to right triangle ABC with C = 90degrees. Given a= 2 and b=√5 Find the six trigonometric functions of A. and find the angles A and B
In terms of angle A, the adjacent is √5, the opposite is 2, and the hypotenuse is 3
so
sinA = opposite/hypotenuse = 2/3
etc.
(you should definitely know the definitions of the trig ratios)
for angle A
sin^-1 (2/3) = 41.8°
B = 90-A = .....
To find the six trigonometric functions of angle A, we need to determine the values of the opposite side, the adjacent side, and the hypotenuse of the right triangle.
In this case, we are given the lengths of sides a and b, where a = 2 and b = √5.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of the hypotenuse:
a^2 + b^2 = c^2
2^2 + (√5)^2 = c^2
4 + 5 = c^2
c^2 = 9
c = 3
Now that we know the lengths of all three sides, we can find the six trigonometric functions:
1. sine (sin A) = opposite/hypotenuse = b/c = √5/3
2. cosine (cos A) = adjacent/hypotenuse = a/c = 2/3
3. tangent (tan A) = opposite/adjacent = b/a = (√5)/2
4. cosecant (csc A) = 1/sin A = 1/(√5/3) = 3/√5
5. secant (sec A) = 1/cos A = 1/(2/3) = 3/2
6. cotangent (cot A) = 1/tan A = 1/((√5)/2) = 2/√5
To find angles A and B, we can use inverse trigonometric functions:
1. angle A = sin^(-1) (sin A) = sin^(-1) (√5/3)
2. angle B = 90 degrees - angle A
Using a calculator or a trigonometric table, you can find the value of angle A in degrees and then calculate angle B based on the fact that the three angles in a triangle add up to 180 degrees.