Evaluate sec30° which of the following is it
a. √3/2
b. 2/√3
c.1/2
d. 2
help
So your answer would be B
You should know the reciprocal identity: sec(theta) = 1/cos(theta)
Looking at a unit circle, cos(30°) is √3/2
So sec(30°)=1/cos(30°)=1/(√3/2)=2/√3
Hopefully, that made sense. Please ask more questions if you have any.
thanks!
NP!
To evaluate sec(30°), we need to understand that secant is the reciprocal of the cosine function. We can use the following formula:
sec(x) = 1/cos(x)
In this case, x is 30°. So, we need to find the value of cos(30°) first.
To evaluate cos(30°), we can use the trigonometric special triangle or unit circle.
In the special triangle, we have an isosceles right triangle with side lengths 1, 1, and √2. By dividing it in half, we get two 30°-60°-90° triangles.
The side opposite the 30° angle is 1, and the hypotenuse is √2.
Therefore, cos(30°) = adjacent/hypotenuse = 1/√2 = √2/2.
Now, to find sec(30°), we take the reciprocal:
sec(30°) = 1/cos(30°) = 1/(√2/2) = 2/√2 = 2/(√2 × √2) = 2/√4.
Simplifying further, we can deduce that √4 = 2:
sec(30°) = 2/√4 = 2/2 = 1.
So, the correct answer is c. 1/2.