1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alex41 [277]
3 years ago
7

Is sin theta=5/6, what are the values of cos theta and tan theta?

Mathematics
1 answer:
mina [271]3 years ago
5 0

let's bear in mind that sin(θ) in this case is positive, that happens only in the I and II Quadrants, where the cosine/adjacent are positive and negative respectively.

\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{6}}\qquad \impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{6^2-5^2}=a\implies \pm\sqrt{36-25}\implies \pm \sqrt{11}=a \\\\[-0.35em] ~\dotfill

\bf cos(\theta )=\cfrac{\stackrel{adjacent}{\pm\sqrt{11}}}{\stackrel{hypotenuse}{6}} \\\\\\ tan(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{adjacent}{\pm\sqrt{11}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{tan(\theta )=\pm\cfrac{5}{\sqrt{11}}\cdot \cfrac{\sqrt{11}}{\sqrt{11}}\implies tan(\theta )=\pm\cfrac{5\sqrt{11}}{11}}

You might be interested in
38 over 14 in simplest form
s344n2d4d5 [400]
38/14= 2 10/14= 2 5/7
The answer is 2 5/7
6 0
3 years ago
Read 2 more answers
1.
wariber [46]

Answer:

b

Step-by-step explanation:

5 0
2 years ago
Question 2 of 10
RideAnS [48]

Answer: 264,615

Step-by-step explanation:apex

5 0
3 years ago
10 x 12 – 14 + 2 + 15 =​
kolbaska11 [484]

Answer:

Your answer of 10 x 12 - 14 +2+15 =123

8 0
3 years ago
Who invented the word "book?"
jarptica [38.1K]
Wow!!thats a word from the old english that made it
7 0
3 years ago
Other questions:
  • 7x + 2y > -5. (1,1)
    10·1 answer
  • Paul and Brett went to math class and were given the same expression to simplify. The expression they were given was 6 + 12 divi
    15·1 answer
  • One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of
    5·1 answer
  • 20 ounces of cereal for 4.40 or 16 ounces of the same brand for 3.68 which is the better buy
    15·1 answer
  • Two of the greatest Greek mathematics were Archimedes (287-212 B.C) and Pythagoras (569-500 BC).
    6·1 answer
  • 4w=276 I'm confused please help me
    6·1 answer
  • Please help Magan recorded the grade-level and instrument of everyone in the middle school
    9·1 answer
  • A coffee machine is designed to discharge, when operating properly, 7 oz. of coffee per cup with a standard deviation of .2 oz.
    7·1 answer
  • Another Giveaway! 60 points!
    5·2 answers
  • Simplest form please!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!