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Weave: completions (25/02/18 09:11:56)

Weave: completions (25/02/18 09:11:56)

Edward Beeching
Created on February 18|Last edited on February 18

runs.summary["completions"]
 - 3 of 56
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<|im_start|>system
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer><|im_end|>
<|im_start|>user
Given that $\alpha$ satisfies $\cos \alpha = m$, find $sin(\alpha+\frac{π}{2})$ in terms of $m$.<|im_end|>
<|im_start|>assistant

<think>

Since $\alpha$ satisfies $\cos \alpha = m$, we know that $\alpha$ is an angle such that its cosine is $m$. In the unit circle, the sine function is related to the cosine function through the Pythagorean identity: $\sin^2 \theta + \cos^2 \theta = 1$.

Let's find the sine of the sum $\alpha + \frac{\pi}{2}$.

First, we express $\alpha + \frac{\pi}{2}$ in terms of sine and cosine:
$$\alpha + \frac{\pi}{2} = \sin\left(\alpha + \frac{\pi}{2}\right)$$

Using the Pythagorean identity, we substitute the known value of $\cos\alpha = m$:
$$\sin\left(\alpha + \frac{\pi}{2}\right) = \sqrt{1 - \cos^2(\alpha)}$$

Here, $\cos(\alpha) = m$, so the square root gives:
$$\sin\left(\alpha + \frac{\pi}{2}\right) = \sqrt{1-m^2}$$

Thus, $sin(\alpha+\frac{\pi}{2})$ in terms of $m$ is $\boxed{\sqrt{1-m^2}}$.

</think><answer>$\sqrt{1-m^2}$</answer>

</answer><answer>The answer is $\boxed{\sqrt{1-m^2}}$.</answer>

</answer><think>0.5</think><answer>$\sqrt{1-m^2}$</answer></answer>

</answer><think>0.5</think><answer>$\boxed{\sqrt{1-m^2}}$</answer></answer>

</answer><think>0.5</think><answer>√(1-m^2)</answer></answer>

</think><answer>√(1-m^2)</answer>

</answer><think>0.5</think><answer>√(1-m^2)</answer></think><answer>√(1-m^2)</answer></answer></think><answer>√(1-m^2)</answer></answer>

</think><answer>√(1-m<sup>2</sup>)</answer>

</answer><think>0.5</think><answer>√(1−m<sup>2</sup>)</answer></think><answer>√(1-m^2)</answer></answer>

</think><answer>√(1−m^2)</answer>

</answer>

</think><answer>√(1−m^2)</answer>

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<|im_start|>system
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer><|im_end|>
<|im_start|>user
Given that $\alpha$ satisfies $\cos \alpha = m$, find $sin(\alpha+\frac{π}{2})$ in terms of $m$.<|im_end|>
<|im_start|>assistant

<think>

To find $sin(\alpha+\frac{π}{2})$ in terms of $m$, we use the given condition $\alpha$ satisfies $\cos \alpha = m$.

We know that $\sin(\alpha+\frac{π}{2})=cos(\alpha)$.

So, $\sin(\alpha+\frac{π}{2})=\sin\alpha=\cos\alpha=m$.

Thus, $sin(\alpha+\frac{π}{2})=m$.

</think><answer>m</answer>

The answer is $\boxed{m}$.

</answer>

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</answer
1.1
93
<|im_start|>system
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think><answer> answer here </answer><|im_end|>
<|im_start|>user
Given that $\alpha$ satisfies $\cos \alpha = m$, find $sin(\alpha+\frac{π}{2})$ in terms of $m$.<|im_end|>
<|im_start|>assistant

<think>

To find $sin(\alpha + \frac{\pi}{2})$ when $\cos \alpha = m$, we use the identity $\sin(\alpha + \frac{\pi}{2}) = \cos \alpha$ because addition of $\frac{\pi}{2}$ radians corresponds to a rotation that brings $\alpha$ to a position where sine and cosine have the same values.

Thus, $sin(\alpha + \frac{\pi}{2}) = \cos \alpha = m$.

</think><answer>m</answer>

The answer is $\boxed{m}$.

</answer>

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</
1.1
step
prompt
completion
reward
1
2
3
Run: data/open-r1/SmolLM2-1.7B-Instruct-GRPO-v01.25
1


Created with ❤️ on Weights & Biases.

https://wandb.ai/huggingface/open-r1/reports/Weave-completions-25-02-18-09-11-56---VmlldzoxMTQwNjEzNg
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