Pythagorean trigonometric identity Puns

A tower casts a shadow that is 160 feet long at a particular time one morning. With the base of the tower at the origin, east as the positive x-axis, and north as the positive y-axis, the shadow at this time is in the northwest quadrant formed by the axes. Also at this time, the tangent of the angle of rotation measured so that the shadow lies in the terminal ray is tan θ = -2.545. What are the coordinates of the tip of the shadow to the nearest foot, and what do they indicate?

I am unsure of how to find the coordinates of the tangent. Since the shadow lies in Quadrant II, is the question asking me to find the cos θ and sin θ, then solve using sin θ/cos θ? That’s all the questions I have, thank you!

and just all trig identities in general

Hello everyone,

Long time reader first time contributor!

When comparing the process of two examples, A) ∫sin³(x)cos⁴(x)dx and B) ∫cos⁴(x)dx, example A splits the sin into ∫sin²(x)cos⁴(x)sin(x)dx which then uses Pythagorean identity to replace the sin²(x) with (1-cos²(x). However, in example B cos⁴x is replaced with a half identity and squaring that ((1+cos(2x))/2)².

I initially thought because of even/odd exponents of the argument but have noticed that not be the case when working out problems like ∫sin⁴(6x)dx

Thank you for your time.

The Pythagorean trigonometric identities that I'm referring to state that:

• tan^2 (x) + 1 = sec^2 (x)
• cot^2 (x) + 1 = csc^2 (x)

But do they have to be squared? Can tan(x) + 1 = sec(x), or cot(x) + 1 = csc(x)?

hi, so I am stuck in this problem to prove left side = right side of Trigonometric identities. I have tried several times but failed to get the right answer.

here's the problem - https://www.reddit.com/user/bidhanko/comments/s1hax0/_/?utm_medium=android_app&utm_source=share

[1+sinA/cosA + cosA/1+sinA = 2secA]

"Prove that left side = right side"

[Here's a screenshot I couldn't figure out how to simplify to get the answer](https://i.ibb.co/r0JMFmc/Image-3.png)

Hello I have a math question which asks me to find the value of cos(195) without any decimal points using the sum or differences trigonometric identity, I don't know where to look for that identity or any for that matter and I want to know what they are and how they interact with one another. thank you

question:

Use a sum or difference identity to find the exact value of each expression: Note: You are not allowed to use decimals in your answer.

cos(195)=?

edit: thanks for everyone's help but I cant me the answer be equivalent to the real answer -0.9659258263's equivalent fraction (i think in radians, but it cant have degrees) Tried it a bunch of different ways but no luck.

i hate my class so much because there's 0 teaching; read a textbook, watch a 5-10 minute video then hopefully know everything.

1. https://prnt.sc/20ds3jq
2. https://prnt.sc/20ds49s
3. https://prnt.sc/20ds4zl
4. https://prnt.sc/20ds68q
5. https://prnt.sc/20ds728

NOTE: This is not a last minute assignment I want anyone to complete, I just have NO IDEA HOW TO EVEN START TO SOLVE THESE QUESTIONS!!!!!! So even helping out in a question or two is appreciated. I literally am learning NOTHING.

https://i.imgur.com/k7cQQzY.png

Question: sec(x)+1/tan(x) = tan(x)/sec(x)-1

How do I prove if this is correct? I’ve tried working with one side to see which one worked, but ended up still with nothing.

These are all different labels.

Trigonometric Ratios, Trigonometric Identities, Trigonometric Functions

I'm not sure if they all mean the same thing because I know some are or is it a category system. From where I've read about they do sure come across as vague and doesn't explain exactly what is the difference of these

i was wondering if i can write all the trigonometric identities and ratios in the boards before starting the exam

The key to being able to rederive every formula by yourself is understanding. When you understand something you don't need to remember lots of detail but just the key ideas. When I was a TA in various universities I encountered many strong students that struggled with remembering trigonometric identities and how to derive the one they needed. They all complained that there are so many of them. Well here is a video that will teach you just that.

https://www.youtube.com/watch?v=sjNFRP25GvY&ab_channel=Math%2CPhysics%2CEngineeringAfter watching it I promise you will be able to rederive every identity yourself and will forever remember its proof.

Hello, how do I prove sin²θsec²θ= sec²θ - 1 ?

The key to being able to rederive every formula by yourself is understanding. When you understand something you don't need to remember lots of detail but just the key ideas. When I was a TA in various universities I encountered many strong students that struggled with remembering trigonometric identities and how to derive the one they needed. They all complained that there are so many of them. Well here is a video that will teach you just that.

https://studio.youtube.com/video/sjNFRP25GvY/analytics/tab-overview/period-default

After watching it I promise you will be able to rederive every identity yourself and will forever remember its proof.