Finding the Value of $r$
We are given two equations:
- $r\sin\theta = \frac{7}{2}$
- $r\cos\theta = \frac{7\sqrt{3}}{2}$
To find the value of $r$, we can square both equations and add them together.
Step 1: Square the equations
Squaring the first equation:
$(r\sin\theta)^2 = \left(\frac{7}{2}\right)^2$ $r^2\sin^2\theta = \frac{49}{4}$Squaring the second equation:
$(r\cos\theta)^2 = \left(\frac{7\sqrt{3}}{2}\right)^2$ $r^2\cos^2\theta = \frac{49 \times 3}{4} = \frac{147}{4}$Step 2: Add the squared equations
Add the results from Step 1:
$r^2\sin^2\theta + r^2\cos^2\theta = \frac{49}{4} + \frac{147}{4}$Step 3: Apply Trigonometric Identity
Factor out $r^2$ and use the identity $\sin^2\theta + \cos^2\theta = 1$:
$r^2(\sin^2\theta + \cos^2\theta) = \frac{49 + 147}{4}$ $r^2(1) = \frac{196}{4}$ $r^2 = 49$Step 4: Solve for $r$
Take the square root of both sides. Since $r$ typically represents a distance or magnitude, we consider the positive root:
$r = \sqrt{49}$ $r = 7$The value of $r$ is 7.
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The given equation can be reduced to
If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?
Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180 / π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π / 9 results. The angle θ must be equal to
What is sin 2α equal to?
If \(\sin θ = \frac{8}{{17}}\) , then find the value of tan θ.
