![student176](/avatars/46592.jpg)
student176
01.04.2021 •
Mathematics
Solve 2 sin 20 - tan 20 = 0 for 0 in [0°, 360°).
Any help would be really appreciated!
Solved
Show answers
More tips
- W Work and Career How much does an honest traffic police officer earn in a day?...
- G Goods and services How to sew a ribbon: Tips for beginners...
- L Leisure and Entertainment How to Learn to Draw Graffiti: Tips for Beginners...
- F Family and Home How to Remove Tar Stains: Tips and Recommendations from Experts...
- F Family and Home How to Remove Fading from Clothes: Tips and Tricks...
- S Sport How to Do a Jumping Split...
- H Health and Medicine How Did Inna Lose Weight on Dom 2?...
- F Family and Home How to Properly Fold Napkins in a Napkin Holder?...
- F Food and Cooking How to Set Up Ventrilo - The Ultimate Guide...
- S Science and Technology How to Make a Homemade Smoker: The Ultimate Guide...
Answers on questions: Mathematics
- L Law Match the vocab word with the correct definition. 1. common ratio a line on the coordinate plane from which graphed data is measured 2. arithmetic sequence the ratio of...
- H History In what ways did radio broadcasting transform American lifestyles?...
- E English Read the excerpt from The Diary of Anne Frank and answer the question that follows. Peter (to MIEP). Maybe Mouschi went back to our house . . . they say that cats . ....
- M Mathematics Pls show how you did it I really need help it’s due tomorrow! PLEASE HELPPP...
Ответ:
Step-by-step explanation:
If there is a character you cannot type, such as θ, you are better off substituting a different letter, or describing it in words. For example, write it as "sinA" or "sin(theta)"
Never use 0 as a substitute for θ! 0 is a constant with a specific value.
Since the argument of the trig functions is an expression, you should put parentheses around it: sin(2A).
I used several trigonometric identities for this question:
Double-angle formula for sine: sin(2θ) = 2sinθcosθ
Double-angle formula for tangent: tan(2θ) = 2tanθ/(1-tan²θ)
Quotient identity: tanθ = sinθ/cosθ
Reciprocal identity: secθ = 1/cosθ
Pythagorean identity: 1+tan²θ = sec²θ
2sin(2θ) - tan(2θ) = 0
2sin(2θ) = tan(2θ)
2·2sinθcosθ = 2tanθ/(1-tan²θ)
2sinθcosθ = tanθ/(1-tan²θ)
2sinθcosθ = (sinθ/cosθ ) · 1/(cosθ(1-tan²θ))
2(1-tan²θ) = 1/cos²θ
2(1-tan²θ) = sec²θ
2-2tan²θ) = 1+tan²θ
1 = 3tan²θ
tan²θ = ⅓
tanθ = ±1/√3
θ = 30°, 330°
Ответ: