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:

Which is equal to sin⁡75∘\sin 75^\circ? \newlineChoices: \newline(A) cos⁡25∘\cos 25^\circ\newline(B) cos⁡15∘\cos 15^\circ\newline(C) sin⁡25∘\sin 25^\circ\newline(D) sin⁡15∘\sin 15^\circ

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Geometryright chevron icon
Sine and cosine of complementary anglesright chevron icon

Full solution

Q. Which is equal to sin⁡75∘\sin 75^\circ? \newlineChoices: \newline(A) cos⁡25∘\cos 25^\circ\newline(B) cos⁡15∘\cos 15^\circ\newline(C) sin⁡25∘\sin 25^\circ\newline(D) sin⁡15∘\sin 15^\circ
  1. Recognize Sum of Angles: Recognize that sin⁡75∘\sin 75^\circ can be expressed as the sum of two angles for which we know the sine and cosine values. The sum of angles formula for sine is sin⁡(a+b)=sin⁡(a)cos⁡(b)+cos⁡(a)sin⁡(b)\sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b). We can express 75∘75^\circ as the sum of 45∘45^\circ and 30∘30^\circ, which are angles we know the sine and cosine values for.
  2. Apply Formula to sin⁡75°\sin 75°: Apply the sum of angles formula to sin⁡75°\sin 75°. We have sin⁡75°=sin⁡(45°+30°)=sin⁡(45°)cos⁡(30°)+cos⁡(45°)sin⁡(30°)\sin 75° = \sin(45° + 30°) = \sin(45°)\cos(30°) + \cos(45°)\sin(30°). We know that sin⁡(45°)=cos⁡(45°)=2/2\sin(45°) = \cos(45°) = \sqrt{2}/2, sin⁡(30°)=1/2\sin(30°) = 1/2, and cos⁡(30°)=3/2\cos(30°) = \sqrt{3}/2.
  3. Substitute Known Values: Substitute the known values into the formula. This gives us sin⁡75°=(22)(32)+(22)(12)=(64)+(24)\sin 75° = (\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) + (\frac{\sqrt{2}}{2})(\frac{1}{2}) = (\frac{\sqrt{6}}{4}) + (\frac{\sqrt{2}}{4}).
  4. Simplify Expression: Simplify the expression. We can combine the fractions to get sin⁡75∘=(6+2)/4\sin 75^\circ = (\sqrt{6} + \sqrt{2})/4.
  5. Recognize Matching Trigonometric Function: Recognize that the value of sin⁡75∘\sin 75^\circ we found must be equal to one of the trigonometric functions of the angles given in the choices. We need to find which one matches (6+2)/4(\sqrt{6} + \sqrt{2})/4.
  6. Compare to Choices: Compare the value of sin⁡75°\sin 75° to the choices. We know that sin⁡(90°−x)=cos⁡(x)\sin(90° - x) = \cos(x), so sin⁡75°=cos⁡15°\sin 75° = \cos 15°. Therefore, sin⁡75°\sin 75° is equal to cos⁡15°\cos 15°.

More problems from Sine and cosine of complementary angles

Question
Factor 28+56t+28w 28+56 t+28 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 2(56+112t+56w) 2(56+112 t+56 w) \newlineB 28(1+2t+w) 28(1+2 t+w) \newlinec 4(7+13t+7w) 4(7+13 t+7 w) \newlineD 7(4+8t+4w) 7(4+8 t+4 w)
Get tutor helpright-arrow

Posted 2 months ago

Question
In an election between two candidates Joseph and Judith, 60%60\% of the total number of voters did not vote for Joseph and 50%50\% of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator]\newline(A) 55\newline(B) 1010\newline(C) 2020\newline(D) 3030
Get tutor helpright-arrow

Posted 2 months ago

Question
Jack, Tom, Beth, and Ruth each have a number of marbles. Jack has 1010 marbles, the least, while Tom has 2727 marbles, the highest. Which of the following could be the average of the number of marbles present with all of them, given that no two of them has the same number of marbles?\newlineA) $13A)\ \$13\newlineB) $17B)\ \$17\newlineC) $23C)\ \$23\newlineD) $26D)\ \$26
Get tutor helpright-arrow

Posted 2 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline1−6y+5+6x−5x+4 1-6 y+5+6 x-5 x+4
Get tutor helpright-arrow

Posted 2 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline−1−4y3−2x3+5x+2−7−x3 -1-4 y^{3}-2 x^{3}+5 x+2-7-x^{3}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system:\newlinex+6y=17−x+3y=−8 \begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the sinstem:\newline{x+6y=17 −x+3y=−8\begin{cases} x+6y=17 \ -x+3y=-8 \end{cases}
Get tutor helpright-arrow

Posted 2 months ago

Question
For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline7,−35,175,… 7,-35,175, \ldots \newline−5 -5 \newline−42 -42 \newline−15 -\frac{1}{5} \newline4242
Get tutor helpright-arrow

Posted 2 months ago

Question
For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline4x−1,3x−1,2x−1,..  4 x-1, \quad 3 x-1, \quad 2 x-1, \quad \text {.. } \newline11\newline−x -x \newlinex x \newline−1 -1
Get tutor helpright-arrow

Posted 2 months ago

Question
A curve CC is defined by the parametric equations x(t)=10cos⁡(t)x(t) = 10\cos(t) and y(t)=−2cos⁡(10t)y(t) = -2\cos(10t). Write the equation of the line tangent to CC when t=7π6t = \frac{7\pi}{6}.
Get tutor helpright-arrow

Posted 1 hour ago

View all (36)