Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

solve for xx cos⁡x+sin⁡x=2\cos x +\sin x = \sqrt{2}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Domain and range of square root functions: equationsright chevron icon

Full solution

Q. solve for xx cos⁡x+sin⁡x=2\cos x +\sin x = \sqrt{2}
  1. Recognize Equality Condition: Recognize that cos⁡(x)\cos(x) and sin⁡(x)\sin(x) are equal when xx is 4545 degrees or π4\frac{\pi}{4} radians.
  2. Use Trigonometric Identity: Use the identity sin⁡(x)=cos⁡(π2−x)\sin(x) = \cos(\frac{\pi}{2} - x) to rewrite the equation as cos⁡(x)+cos⁡(π2−x)=2\cos(x) + \cos(\frac{\pi}{2} - x) = \sqrt{2}.
  3. Substitute xx Value: Since cos⁡(x)=cos⁡(π2−x)\cos(x) = \cos(\frac{\pi}{2} - x) when x=π4x = \frac{\pi}{4}, substitute π4\frac{\pi}{4} into the equation to check if it satisfies the equation.
  4. Calculate Cosine and Sine: Calculate cos⁡(π4)+sin⁡(π4)\cos(\frac{\pi}{4}) + \sin(\frac{\pi}{4}) and see if it equals 2\sqrt{2}.\newlinecos⁡(π4)=22\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} and sin⁡(π4)=22.\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}.
  5. Add Values: Add the values: 2/2+2/2=2\sqrt{2}/2 + \sqrt{2}/2 = \sqrt{2}.
  6. Verify Solution: Since the sum equals 2\sqrt{2}, x=π4x = \frac{\pi}{4} is a solution.

More problems from Domain and range of square root functions: equations

Question
Solve the following equation for y y .\newline2y+5=15−2yy= \begin{array}{l} 2 y+5=\sqrt{15-2 y} \\ y= \\ \end{array}
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve the following equation for w w .\newline5−w4=w+8w= \begin{array}{l} \sqrt{5-\frac{w}{4}}=\sqrt{w+8} \\ w= \end{array}
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve the following equation for z z .\newline4z+9=z+1z=□ \begin{array}{l} \quad \sqrt{4 z+9}=z+1 \\ z=\square \end{array}
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve the following equation for y y .\newline2y−3=3y2−10xy=□ \begin{array}{l} 2 y-3=\sqrt{3 y^{2}-10 x} \\ y=\square \end{array}
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve the following equation for x x .\newline5x−4=x−2x= \begin{array}{l} \sqrt{5 x-4}=x-2 \\ x= \end{array}
Get tutor helpright-arrow

Posted 10 months ago

Question
lim⁡x→32x−5−1x−3= \lim _{x \rightarrow 3} \frac{\sqrt{2 x-5}-1}{x-3}=
Get tutor helpright-arrow

Posted 9 months ago

Question
lim⁡x→−4x+43x+13−1= \lim _{x \rightarrow-4} \frac{x+4}{\sqrt{3 x+13}-1}=
Get tutor helpright-arrow

Posted 9 months ago

Question
lim⁡x→−1x+1x+5−2= \lim _{x \rightarrow-1} \frac{x+1}{\sqrt{x+5}-2}=
Get tutor helpright-arrow

Posted 9 months ago

Question
Let f(x)=x+9 f(x)=\sqrt{x+9} and let c c be the number that satisfies the Mean Value Theorem for f f on the interval [0,16] [0,16] .\newlineWhat is c c ?\newlineChoose 11 answer:\newline(A) 1616\newline(B) 4343\newline(C) 5555\newline(D) 77
Get tutor helpright-arrow

Posted 9 months ago

Question
Let g(x)=5x−1 g(x)=\sqrt{5 x-1} and let c c be the number that satisfies the Mean Value Theorem for g g on the interval [1,10] [1,10] .\newlineWhat is c c ?\newlineChoose 11 answer:\newline(A) 22.2525\newline(B) 44.2525\newline(C) 66.55\newline(D) 88
Get tutor helpright-arrow

Posted 9 months ago

View all (19)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant