what would be the answer when you plug 5pi/4 into this equation 6sec^2x-7sinx for x? i cant get the answer need some help
With what you are not able to calculate the above?
If you are using a calculator, make sure you know how to set the angle input to radians. By default, most calculators work in degrees.
sec²(x)
=sec²(5π/4)
=1/(-sqrt(2)/2)²
=2
sin(5π/4)
=sqrt(2)/2
So
6sec^2x-7sinx = ?
should read:
sin(5π/4)
=-sqrt(2)/2
what would be the answer?
i don't know what would be the answer
Daniel, this is homework help.
Do I understand that you are not able to calculate
6sec^2x-7sinx
when sec(x)^2 and sin(x) have been calculated for you?
Or is it that the answer that you've got does not match?
Please clarify.
6 sec^2 (5?/4) - 7 sin (5?/4) =
= 6 (1/(-1/sqrt(2)))^2 - 7 (-1/sqrt(2))
= 6 (2) + 7/sqrt(2)
= 12 + 7/sqrt(2)
To find the value of x when you plug in 5π/4 into the equation 6sec^2x - 7sinx, you will need to follow a series of steps. Let's break it down:
Step 1: Start by plugging in 5π/4 into the equation:
6sec^2(5π/4) - 7sin(5π/4)
Step 2: Simplify the trigonometric functions:
To simplify secant (sec) and sine (sin), you need to recall their definitions:
- Secant (sec) is the reciprocal of cosine (cos): sec(x) = 1/cos(x)
- Sine (sin) is the ratio of the opposite side to the hypotenuse in a right triangle: sin(x) = opposite/hypotenuse
Step 3: Rewrite sec^2x in terms of cosine (cos):
Since sec(x) = 1/cos(x), sec^2(x) can be rewritten as (1/cos(x))^2, which simplifies to 1/cos^2(x).
Step 4: Substitute the values back into the equation:
Now, the equation becomes:
6(1/cos^2(5π/4)) - 7(sin(5π/4))
Step 5: Simplify further:
Using the trigonometric identity, sin(5π/4) is equal to -sqrt(2)/2, and cos^2(5π/4) is equal to 1/2. Substituting these values into the equation, we get:
6(1/(1/2)) - 7(-sqrt(2)/2)
Simplifying the expression inside the parentheses, we have:
6(2) + 7(sqrt(2)/2)
Multiplying, we get:
12 + 7(sqrt(2)/2)
Simplify the expression by finding a common denominator:
12/1 + (7/2)(sqrt(2)/1)
Now, adding the fractions:
(24/2 + 7(sqrt(2))/2)/1
This results in:
(12 + 7(sqrt(2)))/2
So, when you plug 5π/4 into the equation, the value of x is (12 + 7(sqrt(2)))/2.