- #1
ifomoe
- 5
- 0
Homework Statement
[tex]1/\sqrt{}2 cos 15 - 1/\sqrt{}2 sin 15[/tex]
The Attempt at a Solution
I got [tex]\sqrt{}3/2[/tex].
If anyone could confirm this, I would appreciate it. Thanks.
ifomoe said:Homework Statement
[tex]1/\sqrt{}2 cos 15 - 1/\sqrt{}2 sin 15[/tex]
The Attempt at a Solution
I got [tex]\sqrt{}3/2[/tex].
If anyone could confirm this, I would appreciate it. Thanks.
ifomoe said:Thank you.
Yes. I meant it like that: (1/√2)cos15 - (1/√2)sin15.
I used the reduction formula but I just re-did it and got 1/2.
HallsofIvy said:[tex]sin(x/2)= \sqrt{\frac{1}{2}(1- cos(x))}[/tex]
so
[tex]sin(15)= \sqrt{\frac{1}{2}(1- cos(30))}= \sqrt{\frac{1}{2}\left(1- \frac{\sqrt{3}}{2}\right)}[/tex]
The exact value of a trigonometric equation is a specific numerical value that satisfies the equation. This value can be calculated using trigonometric identities and properties.
To find the exact value of a trigonometric equation, you can use a calculator or a table of trigonometric values. You can also use trigonometric identities and properties to simplify the equation and determine the exact value.
Sure, for example, if we have the equation sin(45°), we can use a calculator or a table to find the exact value, which is 0.70710678118. We can also use the half-angle identity for sine to simplify the equation to √(2)/2, which is the exact value.
Knowing the exact value of a trigonometric equation is important in many real-world applications, such as engineering, physics, and navigation. It allows us to make accurate calculations and predictions based on the given equation.
Yes, there are various trigonometric identities and properties that can be used to simplify equations and find the exact value. For example, the sum and difference identities, double-angle identities, and half-angle identities can all be helpful in finding the exact value of a trigonometric equation.