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
alexgriva [62]
3 years ago
15

What values for θ (0≤θ≤2π) θ ( 0 ≤ θ ≤ 2 π ) satisfy the equation: cos(θ) − tan(θ)cos(θ) = 0

Mathematics
1 answer:
timama [110]3 years ago
6 0

When solving this problem any trigonometric equation, putting things in terms of sines and cosines is a good first step - mainly since most identities are built off these two functions.


cos \theta - (\frac{sin\theta}{cos\theta} * cos\theta) = 0


The cosines after the minus sign divide out leaving us with cos  \theta - sin \theta = 0.


If we subtract the sine to the other side, we are then asking a question: when are the cosine and the sine of angle equal? One common occurence is the 45 - 45 - 90 triangle when the cosine and sine of each angle is the same. So at 45 degrees, or \frac{\pi}{4} radians that happens. Saying this only tells half the story.


We now need to find when the sine and cosine have the same sign (since two negatives would work). Let's work quadrant by quadrant.

Quadrant I - sine and cosine are positive.

Quadrant II - sine is positive, cosine is negative

Quadrant III - cosine is negative, sine is negative

Quadrant IV - cosine is positive, sine is negative.


The 45-45-90 triangle is the Quadrant I response of 45 degrees. The quadrant III angle would be at 180 degrees plus that or 225 degrees. Since the problem is in radians, it would be [tex] \frac{\pi}{4} [/tex] and \frac{\5pi}{4} since we add π radians to get around the unit circle.



You might be interested in
Find the value using identities (302)3
Arlecino [84]

Answer:

108,000,934

1.08934×10^8

Step-by-step explanation:

(302)^3

(a+b)^3

(a+b)^3==a^3+3a^2b+3ab^2+b^3

(300+2)

(300)^3+3(300^2+2)+3(300+2^2)+2^3

27,000,000+81,000,002+8+924

108,000,002+8+924

108,000,934 or 1.08934×10^8

8 0
2 years ago
Unit 6. 14) Please help. Consider a standard deck of 52 playing cards with 4 suits.
aliya0001 [1]

Answer:

The best answer for this is D.) 4/13

8 0
2 years ago
I'm spending lots of points so please help ahaha-
umka2103 [35]
(2x+24)
(11b-33)
(8s-8)
(36+6y)
(25z-100)
(35w-70)
5 0
3 years ago
Read 2 more answers
In a partial variation, the value of<br> is constant.<br> X<br> True<br> False
Sidana [21]

Answer:

need more info

Step-by-step explanation:

7 0
2 years ago
Need Help with 44.. picture above
Daniel [21]

Answer:

Ok:

Step-by-step explanation:

I see that you set up 90 miles = 60 mph * t, where you found out that t = 1.5. What what you needed to do was set 180 miles = 45 mph * t. This is because it is 45 mph for the <em>whole</em> trip. Then, you find that t = 4 hours. That that means that he spent 2.5 hours driving back. Then, we can do d=vt and find 90/2.5 as the speed he went home at. Which comes out to be 36 mph.

8 0
3 years ago
Other questions:
  • What is the value of each number in 1,567.209?
    6·2 answers
  • 3 divided by 5 (step by step)<br><br>​
    13·1 answer
  • For every pizza Eric's family ate, eric ate2 of the 8 pieces. If Eric's family bought 2 pizzas, write the ratio of the total num
    14·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B36%5D%7B540%7D%20" id="TexFormula1" title=" \sqrt[36]{540} " alt=" \sqrt[36]{540}
    10·1 answer
  • What is the center of the circle? Please show steps!
    14·1 answer
  • For g(x)= 1/5x^2+3x, find g'(1)<br> a. -1/4<br> b. 1/4<br> c. -7/4<br> d. -4/7<br> e. 7/4
    6·1 answer
  • 5x - 2x+3=24. HELP ASAP PLS​
    14·1 answer
  • After a 20% discount and 5% sales tax, a book costs $16.80. What was the original price of the book?
    11·1 answer
  • The monthly interest rate payable on Jessica’s credit card is 1.15%. What is the APR
    13·1 answer
  • MULTIPLE CHOICE PLEASE HELP
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!