Pregunta
- Use the special angles to evaluate:
a)
b)
c)
d)
e)
a)
b)
c)
d)
e)
Ask by Conner Cummings. in South Africa
Mar 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
a) The expression is undefined because
is undefined.
b)
c)
d)
e)
Solución
Let’s evaluate each part step by step using the special angles.
a)
-
Calculate
: -
is undefined (since ).
-
-
Calculate
: -
.
-
-
Calculate
: -
.
-
-
Calculate
: -
.
-
-
Combine the results:
- Since
is undefined, the entire expression is undefined.
- Since
b)
-
Calculate
: -
. - Therefore,
.
-
-
Calculate
: -
. - Therefore,
.
-
-
Combine the results:
-
.
-
c)
-
Calculate
: -
. - Therefore,
.
-
-
Combine the results:
-
.
-
d)
-
Calculate
: -
. - Therefore,
.
-
-
Calculate
: -
. - Therefore,
.
-
-
Calculate
: -
. - Therefore,
.
-
-
Combine the results:
-
.
-
e)
-
Calculate
: -
.
-
-
Calculate
: -
.
-
-
Calculate
: -
.
-
-
Combine
: -
.
-
-
Calculate
: -
and . - Therefore, ( \operatorname{cosec} 45^{\circ} \cdot \cos 45^{\
-
Respondido por UpStudy AI y revisado por un tutor profesional
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Extra Insights
First additional information: Did you know that many of those special angles come from triangles that have remarkable properties? For instance, the
triangle has side ratios of
, making it super handy when calculating trigonometric functions! These magical ratios open the door to simplicity, especially if you’re gearing up for tests or trying to impress your friends with some rapid calculations.
Second additional information: Trigonometric identities are like the Swiss Army knives in the world of math! They’re not just helpful for crunching numbers on a test, but they also make life easier while solving real-world problems like engineering designs or physics phenomena. So, whether you’re drawing up blueprints or calculating the trajectory of a basketball, these functions and identities are your trusty companions, ready to help you shine!

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