if sin alpha is 0.28° where 0° is less than or equal to alpha less than or equal to 90°, evaluate cos alpha, tan alpha, sec alpha, cosec alpha and cot alpha. please help, it's urgent.
I'll use a for alpha. sin(a) is not measured in degrees.
sin a = 0.28
since sin^2+cos^2=1, cos a = 0.96
now just use those two values to get all the rest, using the trig function definitions.
To evaluate the trigonometric functions for a given angle, we can use the relationships between these functions and the given value of sin alpha.
Given sin alpha = 0.28°, we need to find cos alpha, tan alpha, sec alpha, cosec alpha, and cot alpha.
Let's start by determining the values of cos alpha and tan alpha:
1. cos alpha = sqrt(1 - sin^2 alpha)
Since sin alpha is given as 0.28°, we can substitute this value into the equation:
cos alpha = sqrt(1 - (0.28)^2)
cos alpha = sqrt(1 - 0.0784)
cos alpha ≈ sqrt(0.9216)
cos alpha ≈ 0.959
2. tan alpha = sin alpha / cos alpha
tan alpha = 0.28° / 0.959
tan alpha ≈ 0.292
Now, we can find sec alpha, cosec alpha, and cot alpha using the reciprocal relationships with cos alpha, sin alpha, and tan alpha:
3. sec alpha = 1 / cos alpha
sec alpha = 1 / 0.959
sec alpha ≈ 1.042
4. cosec alpha = 1 / sin alpha
cosec alpha = 1 / 0.28°
cosec alpha ≈ 3.571
5. cot alpha = 1 / tan alpha
cot alpha = 1 / 0.292
cot alpha ≈ 3.425
Therefore, the evaluated values are:
cos alpha ≈ 0.959
tan alpha ≈ 0.292
sec alpha ≈ 1.042
cosec alpha ≈ 3.571
cot alpha ≈ 3.425